#ifndef gtl_btree_container_hpp_
#define gtl_btree_container_hpp_

// ---------------------------------------------------------------------------
// Copyright (c) 2019-2022, Gregory Popovitch - greg7mdp@gmail.com
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Includes work from abseil-cpp (https://github.com/abseil/abseil-cpp)
// with modifications.
//
// Copyright 2018 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ---------------------------------------------------------------------------

#ifdef _MSC_VER
    #pragma warning(push)

    #pragma warning(disable : 4127) // conditional expression is constant
    #pragma warning(disable : 4324) // structure was padded due to alignment specifier
    #pragma warning(disable : 4355) // 'this': used in base member initializer list
    #pragma warning(disable : 4365) // conversion from 'int' to 'const unsigned __int64',
                                    // signed/unsigned mismatch
    #pragma warning(disable : 4514) // unreferenced inline function has been removed
    #pragma warning(disable : 4623) // default constructor was implicitly defined as deleted
    #pragma warning(disable : 4625) // copy constructor was implicitly defined as deleted
    #pragma warning(disable : 4626) // assignment operator was implicitly defined as deleted
    #pragma warning(disable : 4710) // function not inlined
    #pragma warning(disable : 4711) //  selected for automatic inline expansion
    #pragma warning(disable : 4820) // '6' bytes padding added after data member
    #pragma warning(disable : 4868) // compiler may not enforce left-to-right evaluation order in
                                    // braced initializer list
    #pragma warning(disable : 5026) // move constructor was implicitly defined as deleted
    #pragma warning(disable : 5027) // move assignment operator was implicitly defined as deleted
    #pragma warning(disable : 5045) // Compiler will insert Spectre mitigation for memory load if
                                    // /Qspectre switch specified
#endif

#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <limits>
#include <new>
#include <optional>

#include "gtl_base.hpp"
#include "phmap_fwd_decl.hpp"

#if GTL_HAS_COMPARE
    #include <compare>
namespace gtl {
using weak_ordering   = std::weak_ordering;
using strong_ordering = std::strong_ordering;
}
#endif

#include <string_view>

// MSVC constructibility traits do not detect destructor properties and so our
// implementations should not use them as a source-of-truth.
#if defined(_MSC_VER) && !defined(__clang__) && !defined(__GNUC__)
    #define GTL_META_INTERNAL_STD_CONSTRUCTION_TRAITS_DONT_CHECK_DESTRUCTION 1
#endif

namespace gtl {

namespace compare_internal {

using value_type = int8_t;

template<typename T>
struct Fail {
    static_assert(sizeof(T) < 0, "Only literal `0` is allowed.");
};

template<typename NullPtrT = std::nullptr_t>
struct OnlyLiteralZero {
    constexpr OnlyLiteralZero(NullPtrT) noexcept {} // NOLINT

    template<typename T,
             typename = typename std::enable_if_t<std::is_same_v<T, std::nullptr_t> ||
                                                  (std::is_integral_v<T> && !std::is_same_v<T, int>)>,
             typename = typename Fail<T>::type>
    OnlyLiteralZero(T); // NOLINT
};

enum class eq : value_type {
    equal         = 0,
    equivalent    = equal,
    nonequal      = 1,
    nonequivalent = nonequal,
};

enum class ord : value_type { less = -1, greater = 1 };

enum class ncmp : value_type { unordered = -127 };

#if defined(__cpp_inline_variables) && !defined(_MSC_VER)

    #define GTL_COMPARE_INLINE_BASECLASS_DECL(name)

    #define GTL_COMPARE_INLINE_SUBCLASS_DECL(type, name) static const type name;

    #define GTL_COMPARE_INLINE_INIT(type, name, init) inline constexpr type type::name(init)

#else // __cpp_inline_variables

    #define GTL_COMPARE_INLINE_BASECLASS_DECL(name) static const T name;

    #define GTL_COMPARE_INLINE_SUBCLASS_DECL(type, name)

    #define GTL_COMPARE_INLINE_INIT(type, name, init)                                                                  \
        template<typename T>                                                                                           \
        const T compare_internal::type##_base<T>::name(init)

#endif // __cpp_inline_variables

#if !GTL_HAS_COMPARE
// These template base classes allow for defining the values of the constants
// in the header file (for performance) without using inline variables (which
// aren't available in C++11).
template<typename T>
struct weak_equality_base {
    GTL_COMPARE_INLINE_BASECLASS_DECL(equivalent)
    GTL_COMPARE_INLINE_BASECLASS_DECL(nonequivalent)
};

template<typename T>
struct strong_equality_base {
    GTL_COMPARE_INLINE_BASECLASS_DECL(equal)
    GTL_COMPARE_INLINE_BASECLASS_DECL(nonequal)
    GTL_COMPARE_INLINE_BASECLASS_DECL(equivalent)
    GTL_COMPARE_INLINE_BASECLASS_DECL(nonequivalent)
};

template<typename T>
struct partial_ordering_base {
    GTL_COMPARE_INLINE_BASECLASS_DECL(less)
    GTL_COMPARE_INLINE_BASECLASS_DECL(equivalent)
    GTL_COMPARE_INLINE_BASECLASS_DECL(greater)
    GTL_COMPARE_INLINE_BASECLASS_DECL(unordered)
};

template<typename T>
struct weak_ordering_base {
    GTL_COMPARE_INLINE_BASECLASS_DECL(less)
    GTL_COMPARE_INLINE_BASECLASS_DECL(equivalent)
    GTL_COMPARE_INLINE_BASECLASS_DECL(greater)
};

template<typename T>
struct strong_ordering_base {
    GTL_COMPARE_INLINE_BASECLASS_DECL(less)
    GTL_COMPARE_INLINE_BASECLASS_DECL(equal)
    GTL_COMPARE_INLINE_BASECLASS_DECL(equivalent)
    GTL_COMPARE_INLINE_BASECLASS_DECL(greater)
};

} // namespace compare_internal

class weak_equality : public compare_internal::weak_equality_base<weak_equality> {
    explicit constexpr weak_equality(compare_internal::eq v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    friend struct compare_internal::weak_equality_base<weak_equality>;

public:
    GTL_COMPARE_INLINE_SUBCLASS_DECL(weak_equality, equivalent)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(weak_equality, nonequivalent)

    // Comparisons
    friend constexpr bool operator==(weak_equality v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ == 0;
    }
    friend constexpr bool operator!=(weak_equality v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ != 0;
    }
    friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>, weak_equality v) noexcept {
        return 0 == v.value_;
    }
    friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>, weak_equality v) noexcept {
        return 0 != v.value_;
    }

private:
    compare_internal::value_type value_;
};
GTL_COMPARE_INLINE_INIT(weak_equality, equivalent, compare_internal::eq::equivalent);
GTL_COMPARE_INLINE_INIT(weak_equality, nonequivalent, compare_internal::eq::nonequivalent);

class strong_equality : public compare_internal::strong_equality_base<strong_equality> {
    explicit constexpr strong_equality(compare_internal::eq v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    friend struct compare_internal::strong_equality_base<strong_equality>;

public:
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, equal)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, nonequal)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, equivalent)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, nonequivalent)

    // Conversion
    constexpr operator weak_equality() const noexcept { // NOLINT
        return value_ == 0 ? weak_equality::equivalent : weak_equality::nonequivalent;
    }
    // Comparisons
    friend constexpr bool operator==(strong_equality v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ == 0;
    }
    friend constexpr bool operator!=(strong_equality v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ != 0;
    }
    friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>, strong_equality v) noexcept {
        return 0 == v.value_;
    }
    friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>, strong_equality v) noexcept {
        return 0 != v.value_;
    }

private:
    compare_internal::value_type value_;
};

GTL_COMPARE_INLINE_INIT(strong_equality, equal, compare_internal::eq::equal);
GTL_COMPARE_INLINE_INIT(strong_equality, nonequal, compare_internal::eq::nonequal);
GTL_COMPARE_INLINE_INIT(strong_equality, equivalent, compare_internal::eq::equivalent);
GTL_COMPARE_INLINE_INIT(strong_equality, nonequivalent, compare_internal::eq::nonequivalent);

class partial_ordering : public compare_internal::partial_ordering_base<partial_ordering> {
    explicit constexpr partial_ordering(compare_internal::eq v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    explicit constexpr partial_ordering(compare_internal::ord v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    explicit constexpr partial_ordering(compare_internal::ncmp v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    friend struct compare_internal::partial_ordering_base<partial_ordering>;

    constexpr bool is_ordered() const noexcept {
        return value_ != compare_internal::value_type(compare_internal::ncmp::unordered);
    }

public:
    GTL_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, less)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, equivalent)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, greater)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, unordered)

    // Conversion
    constexpr operator weak_equality() const noexcept { // NOLINT
        return value_ == 0 ? weak_equality::equivalent : weak_equality::nonequivalent;
    }
    // Comparisons
    friend constexpr bool operator==(partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.is_ordered() && v.value_ == 0;
    }
    friend constexpr bool operator!=(partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return !v.is_ordered() || v.value_ != 0;
    }
    friend constexpr bool operator<(partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.is_ordered() && v.value_ < 0;
    }
    friend constexpr bool operator<=(partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.is_ordered() && v.value_ <= 0;
    }
    friend constexpr bool operator>(partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.is_ordered() && v.value_ > 0;
    }
    friend constexpr bool operator>=(partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.is_ordered() && v.value_ >= 0;
    }
    friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>, partial_ordering v) noexcept {
        return v.is_ordered() && 0 == v.value_;
    }
    friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>, partial_ordering v) noexcept {
        return !v.is_ordered() || 0 != v.value_;
    }
    friend constexpr bool operator<(compare_internal::OnlyLiteralZero<>, partial_ordering v) noexcept {
        return v.is_ordered() && 0 < v.value_;
    }
    friend constexpr bool operator<=(compare_internal::OnlyLiteralZero<>, partial_ordering v) noexcept {
        return v.is_ordered() && 0 <= v.value_;
    }
    friend constexpr bool operator>(compare_internal::OnlyLiteralZero<>, partial_ordering v) noexcept {
        return v.is_ordered() && 0 > v.value_;
    }
    friend constexpr bool operator>=(compare_internal::OnlyLiteralZero<>, partial_ordering v) noexcept {
        return v.is_ordered() && 0 >= v.value_;
    }

private:
    compare_internal::value_type value_;
};

GTL_COMPARE_INLINE_INIT(partial_ordering, less, compare_internal::ord::less);
GTL_COMPARE_INLINE_INIT(partial_ordering, equivalent, compare_internal::eq::equivalent);
GTL_COMPARE_INLINE_INIT(partial_ordering, greater, compare_internal::ord::greater);
GTL_COMPARE_INLINE_INIT(partial_ordering, unordered, compare_internal::ncmp::unordered);

class weak_ordering : public compare_internal::weak_ordering_base<weak_ordering> {
    explicit constexpr weak_ordering(compare_internal::eq v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    explicit constexpr weak_ordering(compare_internal::ord v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    friend struct compare_internal::weak_ordering_base<weak_ordering>;

public:
    GTL_COMPARE_INLINE_SUBCLASS_DECL(weak_ordering, less)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(weak_ordering, equivalent)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(weak_ordering, greater)

    // Conversions
    constexpr operator weak_equality() const noexcept { // NOLINT
        return value_ == 0 ? weak_equality::equivalent : weak_equality::nonequivalent;
    }
    constexpr operator partial_ordering() const noexcept { // NOLINT
        return value_ == 0 ? partial_ordering::equivalent
                           : (value_ < 0 ? partial_ordering::less : partial_ordering::greater);
    }
    // Comparisons
    friend constexpr bool operator==(weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ == 0;
    }
    friend constexpr bool operator!=(weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ != 0;
    }
    friend constexpr bool operator<(weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ < 0;
    }
    friend constexpr bool operator<=(weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ <= 0;
    }
    friend constexpr bool operator>(weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ > 0;
    }
    friend constexpr bool operator>=(weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ >= 0;
    }
    friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>, weak_ordering v) noexcept {
        return 0 == v.value_;
    }
    friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>, weak_ordering v) noexcept {
        return 0 != v.value_;
    }
    friend constexpr bool operator<(compare_internal::OnlyLiteralZero<>, weak_ordering v) noexcept {
        return 0 < v.value_;
    }
    friend constexpr bool operator<=(compare_internal::OnlyLiteralZero<>, weak_ordering v) noexcept {
        return 0 <= v.value_;
    }
    friend constexpr bool operator>(compare_internal::OnlyLiteralZero<>, weak_ordering v) noexcept {
        return 0 > v.value_;
    }
    friend constexpr bool operator>=(compare_internal::OnlyLiteralZero<>, weak_ordering v) noexcept {
        return 0 >= v.value_;
    }

private:
    compare_internal::value_type value_;
};

GTL_COMPARE_INLINE_INIT(weak_ordering, less, compare_internal::ord::less);
GTL_COMPARE_INLINE_INIT(weak_ordering, equivalent, compare_internal::eq::equivalent);
GTL_COMPARE_INLINE_INIT(weak_ordering, greater, compare_internal::ord::greater);

class strong_ordering : public compare_internal::strong_ordering_base<strong_ordering> {
    explicit constexpr strong_ordering(compare_internal::eq v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    explicit constexpr strong_ordering(compare_internal::ord v) noexcept
        : value_(static_cast<compare_internal::value_type>(v)) {}
    friend struct compare_internal::strong_ordering_base<strong_ordering>;

public:
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, less)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, equal)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, equivalent)
    GTL_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, greater)

    // Conversions
    constexpr operator weak_equality() const noexcept { // NOLINT
        return value_ == 0 ? weak_equality::equivalent : weak_equality::nonequivalent;
    }
    constexpr operator strong_equality() const noexcept { // NOLINT
        return value_ == 0 ? strong_equality::equal : strong_equality::nonequal;
    }
    constexpr operator partial_ordering() const noexcept { // NOLINT
        return value_ == 0 ? partial_ordering::equivalent
                           : (value_ < 0 ? partial_ordering::less : partial_ordering::greater);
    }
    constexpr operator weak_ordering() const noexcept { // NOLINT
        return value_ == 0 ? weak_ordering::equivalent : (value_ < 0 ? weak_ordering::less : weak_ordering::greater);
    }
    // Comparisons
    friend constexpr bool operator==(strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ == 0;
    }
    friend constexpr bool operator!=(strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ != 0;
    }
    friend constexpr bool operator<(strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ < 0;
    }
    friend constexpr bool operator<=(strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ <= 0;
    }
    friend constexpr bool operator>(strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ > 0;
    }
    friend constexpr bool operator>=(strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept {
        return v.value_ >= 0;
    }
    friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>, strong_ordering v) noexcept {
        return 0 == v.value_;
    }
    friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>, strong_ordering v) noexcept {
        return 0 != v.value_;
    }
    friend constexpr bool operator<(compare_internal::OnlyLiteralZero<>, strong_ordering v) noexcept {
        return 0 < v.value_;
    }
    friend constexpr bool operator<=(compare_internal::OnlyLiteralZero<>, strong_ordering v) noexcept {
        return 0 <= v.value_;
    }
    friend constexpr bool operator>(compare_internal::OnlyLiteralZero<>, strong_ordering v) noexcept {
        return 0 > v.value_;
    }
    friend constexpr bool operator>=(compare_internal::OnlyLiteralZero<>, strong_ordering v) noexcept {
        return 0 >= v.value_;
    }

private:
    compare_internal::value_type value_;
};
GTL_COMPARE_INLINE_INIT(strong_ordering, less, compare_internal::ord::less);
GTL_COMPARE_INLINE_INIT(strong_ordering, equal, compare_internal::eq::equal);
GTL_COMPARE_INLINE_INIT(strong_ordering, equivalent, compare_internal::eq::equivalent);
GTL_COMPARE_INLINE_INIT(strong_ordering, greater, compare_internal::ord::greater);

    #undef GTL_COMPARE_INLINE_BASECLASS_DECL
    #undef GTL_COMPARE_INLINE_SUBCLASS_DECL
    #undef GTL_COMPARE_INLINE_INIT

namespace compare_internal {
#endif // !GTL_HAS_COMPARE

// We also provide these comparator adapter functions for internal gtl use.

// Helper functions to do a boolean comparison of two keys given a boolean
// or three-way comparator.
// SFINAE prevents implicit conversions to bool (such as from int).
// ----------------------------------------------------------------------
template<typename BoolType, std::enable_if_t<std::is_same_v<bool, BoolType>, int> = 0>
constexpr bool compare_result_as_less_than(const BoolType r) {
    return r;
}

constexpr bool compare_result_as_less_than(const gtl::weak_ordering r) { return r < 0; }

template<typename Compare, typename K, typename LK>
constexpr bool do_less_than_comparison(const Compare& compare, const K& x, const LK& y) {
    return compare_result_as_less_than(compare(x, y));
}

// Helper functions to do a three-way comparison of two keys given a boolean or
// three-way comparator.
// SFINAE prevents implicit conversions to int (such as from bool).
// ---------------------------------------------------------------------------
template<typename Int, std::enable_if_t<std::is_same_v<int, Int>, int> = 0>
constexpr gtl::weak_ordering compare_result_as_ordering(const Int c) {
    return c < 0 ? gtl::weak_ordering::less : c == 0 ? gtl::weak_ordering::equivalent : gtl::weak_ordering::greater;
}

constexpr gtl::weak_ordering compare_result_as_ordering(const gtl::weak_ordering c) { return c; }

template<typename Compare,
         typename K,
         typename LK,
         std::enable_if_t<!std::is_same_v<bool, std::invoke_result_t<Compare, const K&, const LK&>>, int> = 0>
constexpr gtl::weak_ordering do_three_way_comparison(const Compare& compare, const K& x, const LK& y) {
    return compare_result_as_ordering(compare(x, y));
}

template<typename Compare,
         typename K,
         typename LK,
         std::enable_if_t<std::is_same_v<bool, std::invoke_result_t<Compare, const K&, const LK&>>, int> = 0>
constexpr gtl::weak_ordering do_three_way_comparison(const Compare& cmp, const K& x, const LK& y) {
    return cmp(x, y)   ? gtl::weak_ordering::less
           : cmp(y, x) ? gtl::weak_ordering::greater
                       : gtl::weak_ordering::equivalent;
}

} // namespace compare_internal

namespace priv {

// A helper class that indicates if the Compare parameter is a key-compare-to
// comparator.
// --------------------------------------------------------------------------
template<typename Compare, typename T>
using btree_is_key_compare_to =
    std::is_convertible<std::invoke_result_t<Compare, const T&, const T&>, gtl::weak_ordering>;

struct StringBtreeDefaultLess {
    using is_transparent = void;

    StringBtreeDefaultLess() = default;

    // Compatibility constructor.
    StringBtreeDefaultLess(std::less<std::string>) {}      // NOLINT
    StringBtreeDefaultLess(std::less<std::string_view>) {} // NOLINT
    StringBtreeDefaultLess(gtl::Less<std::string_view>) {} // NOLINT

    gtl::weak_ordering operator()(std::string_view lhs, std::string_view rhs) const {
        return compare_internal::compare_result_as_ordering(lhs.compare(rhs));
    }
};

struct StringBtreeDefaultGreater {
    using is_transparent = void;

    StringBtreeDefaultGreater() = default;

    StringBtreeDefaultGreater(std::greater<std::string>) {}      // NOLINT
    StringBtreeDefaultGreater(std::greater<std::string_view>) {} // NOLINT

    gtl::weak_ordering operator()(std::string_view lhs, std::string_view rhs) const {
        return compare_internal::compare_result_as_ordering(rhs.compare(lhs));
    }
};

// A helper class to convert a boolean comparison into a three-way "compare-to"
// comparison that returns a negative value to indicate less-than, zero to
// indicate equality and a positive value to indicate greater-than. This helper
// class is specialized for less<std::string>, greater<std::string>,
// less<std::string_view>, and greater<std::string_view>.
//
// key_compare_to_adapter is provided so that btree users
// automatically get the more efficient compare-to code when using common
// google string types with common comparison functors.
// These string-like specializations also turn on heterogeneous lookup by
// default.
// ---------------------------------------------------------------------------
template<typename Compare>
struct key_compare_to_adapter {
    using type = Compare;
};

template<>
struct key_compare_to_adapter<std::less<std::string>> {
    using type = StringBtreeDefaultLess;
};

template<>
struct key_compare_to_adapter<gtl::Less<std::string>> {
    using type = StringBtreeDefaultLess;
};

template<>
struct key_compare_to_adapter<std::greater<std::string>> {
    using type = StringBtreeDefaultGreater;
};

template<>
struct key_compare_to_adapter<std::less<std::string_view>> {
    using type = StringBtreeDefaultLess;
};

template<>
struct key_compare_to_adapter<gtl::Less<std::string_view>> {
    using type = StringBtreeDefaultLess;
};

template<>
struct key_compare_to_adapter<std::greater<std::string_view>> {
    using type = StringBtreeDefaultGreater;
};

template<typename Key, typename Compare, typename Alloc, int TargetNodeSize, bool Multi, typename SlotPolicy>
struct common_params {
    // If Compare is a common comparator for a std::string-like type, then we adapt it
    // to use heterogeneous lookup and to be a key-compare-to comparator.
    // -------------------------------------------------------------------------------
    using key_compare = typename key_compare_to_adapter<Compare>::type;

    // A type which indicates if we have a key-compare-to functor or a plain old
    // key-compare functor.
    // -------------------------------------------------------------------------
    using is_key_compare_to = btree_is_key_compare_to<key_compare, Key>;

    using allocator_type  = Alloc;
    using key_type        = Key;
    using size_type       = std::size_t;
    using difference_type = ptrdiff_t;

    // True if this is a multiset or multimap.
    using is_multi_container = std::integral_constant<bool, Multi>;

    using slot_policy     = SlotPolicy;
    using slot_type       = typename slot_policy::slot_type;
    using value_type      = typename slot_policy::value_type;
    using init_type       = typename slot_policy::mutable_value_type;
    using pointer         = value_type*;
    using const_pointer   = const value_type*;
    using reference       = value_type&;
    using const_reference = const value_type&;

    enum {
        kTargetNodeSize = TargetNodeSize,

        // Upper bound for the available space for values. This is largest for leaf
        // nodes, which have overhead of at least a pointer + 4 bytes (for storing
        // 3 field_types and an enum).
        kNodeSlotSpace = TargetNodeSize - /*minimum overhead=*/(sizeof(void*) + 4),
    };

    // This is an integral type large enough to hold as many
    // ValueSize-values as will fit a node of TargetNodeSize bytes.
    // ------------------------------------------------------------
    using node_count_type =
        std::conditional_t<(kNodeSlotSpace / sizeof(slot_type) > (std::numeric_limits<uint8_t>::max)()),
                           uint16_t,
                           uint8_t>; // NOLINT

    // The following methods are necessary for passing this struct as PolicyTraits
    // for node_handle and/or are used within btree.
    static value_type&       element(slot_type* slot) { return slot_policy::element(slot); }
    static const value_type& element(const slot_type* slot) { return slot_policy::element(slot); }
    template<class... Args>
    static void construct(Alloc* alloc, slot_type* slot, Args&&... args) {
        slot_policy::construct(alloc, slot, std::forward<Args>(args)...);
    }
    static void construct(Alloc* alloc, slot_type* slot, slot_type* other) {
        slot_policy::construct(alloc, slot, other);
    }
    static void destroy(Alloc* alloc, slot_type* slot) { slot_policy::destroy(alloc, slot); }
    static void transfer(Alloc* alloc, slot_type* new_slot, slot_type* old_slot) {
        construct(alloc, new_slot, old_slot);
        destroy(alloc, old_slot);
    }
    static void swap(Alloc* alloc, slot_type* a, slot_type* b) { slot_policy::swap(alloc, a, b); }
    static void move(Alloc* alloc, slot_type* src, slot_type* dest) { slot_policy::move(alloc, src, dest); }
    static void move(Alloc* alloc, slot_type* first, slot_type* last, slot_type* result) {
        slot_policy::move(alloc, first, last, result);
    }
};

// A parameters structure for holding the type parameters for a btree_map.
// Compare and Alloc should be nothrow copy-constructible.
// -----------------------------------------------------------------------
template<typename Key, typename Data, typename Compare, typename Alloc, int TargetNodeSize, bool Multi>
struct map_params : common_params<Key, Compare, Alloc, TargetNodeSize, Multi, gtl::priv::map_slot_policy<Key, Data>> {
    using super_type  = typename map_params::common_params;
    using mapped_type = Data;
    // This type allows us to move keys when it is safe to do so. It is safe
    // for maps in which value_type and mutable_value_type are layout compatible.
    // --------------------------------------------------------------------------
    using slot_policy = typename super_type::slot_policy;
    using slot_type   = typename super_type::slot_type;
    using value_type  = typename super_type::value_type;
    using init_type   = typename super_type::init_type;

    using key_compare = typename super_type::key_compare;
    // Inherit from key_compare for empty base class optimization.
    struct value_compare : private key_compare {
        value_compare() = default;
        explicit value_compare(const key_compare& cmp)
            : key_compare(cmp) {}

        template<typename T, typename U>
        auto operator()(const T& left, const U& right) const
            -> decltype(std::declval<key_compare>()(left.first, right.first)) {
            return key_compare::operator()(left.first, right.first);
        }
    };
    using is_map_container = std::true_type;

    static const Key&   key(const value_type& x) { return x.first; }
    static const Key&   key(const init_type& x) { return x.first; }
    static const Key&   key(const slot_type* x) { return slot_policy::key(x); }
    static mapped_type& value(value_type* value) { return value->second; }
};

// This type implements the necessary functions from the
// btree::priv::slot_type interface.
// -----------------------------------------------------
template<typename Key>
struct set_slot_policy {
    using slot_type          = Key;
    using value_type         = Key;
    using mutable_value_type = Key;

    static value_type&       element(slot_type* slot) { return *slot; }
    static const value_type& element(const slot_type* slot) { return *slot; }

    template<typename Alloc, class... Args>
    static void construct(Alloc* alloc, slot_type* slot, Args&&... args) {
        std::allocator_traits<Alloc>::construct(*alloc, slot, std::forward<Args>(args)...);
    }

    template<typename Alloc>
    static void construct(Alloc* alloc, slot_type* slot, slot_type* other) {
        std::allocator_traits<Alloc>::construct(*alloc, slot, std::move(*other));
    }

    template<typename Alloc>
    static void destroy(Alloc* alloc, slot_type* slot) {
        std::allocator_traits<Alloc>::destroy(*alloc, slot);
    }

    template<typename Alloc>
    static void swap(Alloc* /*alloc*/, slot_type* a, slot_type* b) {
        using std::swap;
        swap(*a, *b);
    }

    template<typename Alloc>
    static void move(Alloc* /*alloc*/, slot_type* src, slot_type* dest) {
        *dest = std::move(*src);
    }

    template<typename Alloc>
    static void move(Alloc* alloc, slot_type* first, slot_type* last, slot_type* result) {
        for (slot_type *src = first, *dest = result; src != last; ++src, ++dest)
            move(alloc, src, dest);
    }
};

// A parameters structure for holding the type parameters for a btree_set.
// Compare and Alloc should be nothrow copy-constructible.
// ------------------------------------------------------------------------
template<typename Key, typename Compare, typename Alloc, int TargetNodeSize, bool Multi>
struct set_params : common_params<Key, Compare, Alloc, TargetNodeSize, Multi, set_slot_policy<Key>> {
    using value_type       = Key;
    using slot_type        = typename set_params::common_params::slot_type;
    using value_compare    = typename set_params::common_params::key_compare;
    using is_map_container = std::false_type;

    static const Key& key(const value_type& x) { return x; }
    static const Key& key(const slot_type* x) { return *x; }
};

// An adapter class that converts a lower-bound compare into an upper-bound
// compare. Note: there is no need to make a version of this adapter specialized
// for key-compare-to functors because the upper-bound (the first value greater
// than the input) is never an exact match.
// -----------------------------------------------------------------------------
template<typename Compare>
struct upper_bound_adapter {
    explicit upper_bound_adapter(const Compare& c)
        : comp(c) {}
    template<typename K, typename LK>
    bool operator()(const K& a, const LK& b) const {
        // Returns true when a is not greater than b.
        return !gtl::compare_internal::compare_result_as_less_than(comp(b, a));
    }

private:
    Compare comp;
};

enum class MatchKind : uint8_t { kEq, kNe };

template<typename V, bool IsCompareTo>
struct SearchResult {
    V         value;
    MatchKind match;

    static constexpr bool HasMatch() { return true; }
    bool                  IsEq() const { return match == MatchKind::kEq; }
};

// When we don't use CompareTo, `match` is not present.
// This ensures that callers can't use it accidentally when it provides no
// useful information.
// -----------------------------------------------------------------------
template<typename V>
struct SearchResult<V, false> {
    V value;

    static constexpr bool HasMatch() { return false; }
    static constexpr bool IsEq() { return false; }
};

// A node in the btree holding. The same node type is used for both internal
// and leaf nodes in the btree, though the nodes are allocated in such a way
// that the children array is only valid in internal nodes.
// -------------------------------------------------------------------------
template<typename Params>
class btree_node {
    using is_key_compare_to  = typename Params::is_key_compare_to;
    using is_multi_container = typename Params::is_multi_container;
    using field_type         = typename Params::node_count_type;
    using allocator_type     = typename Params::allocator_type;
    using slot_type          = typename Params::slot_type;

public:
    using params_type     = Params;
    using key_type        = typename Params::key_type;
    using value_type      = typename Params::value_type;
    using pointer         = typename Params::pointer;
    using const_pointer   = typename Params::const_pointer;
    using reference       = typename Params::reference;
    using const_reference = typename Params::const_reference;
    using key_compare     = typename Params::key_compare;
    using size_type       = typename Params::size_type;
    using difference_type = typename Params::difference_type;

    // Btree decides whether to use linear node search as follows:
    //   - If the key is arithmetic and the comparator is std::less or
    //     std::greater, choose linear.
    //   - Otherwise, choose binary.
    // ---------------------------------------------------------------
    // TODO(ezb): Might make sense to add condition(s) based on node-size.
    using use_linear_search =
        std::integral_constant<bool,
                               std::is_arithmetic_v<key_type> && (std::is_same_v<gtl::Less<key_type>, key_compare> ||
                                                                  std::is_same_v<std::less<key_type>, key_compare> ||
                                                                  std::is_same_v<std::greater<key_type>, key_compare>)>;

    ~btree_node()                            = default;
    btree_node(btree_node const&)            = delete;
    btree_node& operator=(btree_node const&) = delete;

    // Public for EmptyNodeType.
    // -------------------------
    constexpr static size_type Alignment() {
        static_assert(LeafLayout(1).Alignment() == InternalLayout().Alignment(),
                      "Alignment of all nodes must be equal.");
        return (size_type)InternalLayout().Alignment();
    }

protected:
    btree_node() = default;

private:
    using layout_type = gtl::priv::Layout<btree_node*, field_type, slot_type, btree_node*>;
    constexpr static size_type SizeWithNValues(size_type n) {
        return (size_type)layout_type(/*parent*/ 1,
                                      /*position, start, count, max_count*/ 4,
                                      /*values*/ (size_t)n,
                                      /*children*/ 0)
            .AllocSize();
    }

    // A lower bound for the overhead of fields other than values in a leaf node.
    // --------------------------------------------------------------------------
    constexpr static size_type MinimumOverhead() { return (size_type)(SizeWithNValues(1) - sizeof(value_type)); }

    // Compute how many values we can fit onto a leaf node taking into account
    // padding.
    // -----------------------------------------------------------------------
    constexpr static size_type NodeTargetValues(const int begin, const int end) {
        return begin == end ? begin
               : SizeWithNValues((begin + end) / 2 + 1) > params_type::kTargetNodeSize
                   ? NodeTargetValues(begin, (begin + end) / 2)
                   : NodeTargetValues((begin + end) / 2 + 1, end);
    }

    enum {
        kTargetNodeSize   = params_type::kTargetNodeSize,
        kNodeTargetValues = NodeTargetValues(0, params_type::kTargetNodeSize),

        // We need a minimum of 3 values per internal node in order to perform
        // splitting (1 value for the two nodes involved in the split and 1 value
        // propagated to the parent as the delimiter for the split).
        // ----------------------------------------------------------------------
        kNodeValues = kNodeTargetValues >= 3 ? kNodeTargetValues : 3,

        // The node is internal (i.e. is not a leaf node) if and only if `max_count`
        // has this value.
        // -------------------------------------------------------------------------
        kInternalNodeMaxCount = 0,
    };

    // Leaves can have less than kNodeValues values.
    // ---------------------------------------------
    constexpr static layout_type LeafLayout(const int max_values = kNodeValues) {
        return layout_type(/*parent*/ 1,
                           /*position, start, count, max_count*/ 4,
                           /*values*/ (size_t)max_values,
                           /*children*/ 0);
    }
    constexpr static layout_type InternalLayout() {
        return layout_type(/*parent*/ 1,
                           /*position, start, count, max_count*/ 4,
                           /*values*/ kNodeValues,
                           /*children*/ kNodeValues + 1);
    }
    constexpr static size_type LeafSize(const int max_values = kNodeValues) {
        return (size_type)LeafLayout(max_values).AllocSize();
    }
    constexpr static size_type InternalSize() { return (size_type)InternalLayout().AllocSize(); }

    // N is the index of the type in the Layout definition.
    // ElementType<N> is the Nth type in the Layout definition.
    // --------------------------------------------------------
    template<size_type N>
    inline typename layout_type::template ElementType<N>* GetField() {
        // We assert that we don't read from values that aren't there.
        assert(N < 3 || !leaf());
        return InternalLayout().template Pointer<N>(reinterpret_cast<char*>(this));
    }

    template<size_type N>
    inline const typename layout_type::template ElementType<N>* GetField() const {
        assert(N < 3 || !leaf());
        return InternalLayout().template Pointer<N>(reinterpret_cast<const char*>(this));
    }

    void             set_parent(btree_node* p) { *GetField<0>() = p; }
    field_type&      mutable_count() { return GetField<1>()[2]; }
    slot_type*       slot(size_type i) { return &GetField<2>()[i]; }
    const slot_type* slot(size_type i) const { return &GetField<2>()[i]; }
    void             set_position(field_type v) { GetField<1>()[0] = v; }
    void             set_start(field_type v) { GetField<1>()[1] = v; }
    void             set_count(field_type v) { GetField<1>()[2] = v; }
    void             set_max_count(field_type v) { GetField<1>()[3] = v; }

public:
    // Whether this is a leaf node or not. This value doesn't change after the
    // node is created.
    // -----------------------------------------------------------------------
    bool leaf() const { return GetField<1>()[3] != kInternalNodeMaxCount; }

    // Getter for the position of this node in its parent.
    // ---------------------------------------------------
    field_type position() const { return GetField<1>()[0]; }

    // Getter for the offset of the first value in the `values` array.
    // ---------------------------------------------------------------
    field_type start() const { return GetField<1>()[1]; }

    // Getters for the number of values stored in this node.
    // -----------------------------------------------------
    field_type count() const { return GetField<1>()[2]; }
    field_type max_count() const {
        // Internal nodes have max_count==kInternalNodeMaxCount.
        // Leaf nodes have max_count in [1, kNodeValues].
        // -----------------------------------------------------
        const field_type max_cnt = GetField<1>()[3];
        return max_cnt == field_type{ kInternalNodeMaxCount } ? field_type{ kNodeValues } : max_cnt;
    }

    // Getter for the parent of this node.
    // -----------------------------------
    btree_node* parent() const { return *GetField<0>(); }

    // Getter for whether the node is the root of the tree. The parent of the
    // root of the tree is the leftmost node in the tree which is guaranteed to
    // be a leaf.
    // ------------------------------------------------------------------------
    bool is_root() const { return parent()->leaf(); }
    void make_root() {
        assert(parent()->is_root());
        set_parent(parent()->parent());
    }

    // Getters for the key/value at position i in the node.
    // ----------------------------------------------------
    const key_type& key(size_type i) const { return params_type::key(slot(i)); }
    reference       value(size_type i) { return params_type::element(slot(i)); }
    const_reference value(size_type i) const { return params_type::element(slot(i)); }

#if defined(__GNUC__) || defined(__clang__)
    #pragma GCC diagnostic push
    #pragma GCC diagnostic ignored "-Warray-bounds"
#endif
    // Getters/setter for the child at position i in the node.
    // -------------------------------------------------------
    btree_node*  child(size_type i) const { return GetField<3>()[i]; }
    btree_node*& mutable_child(size_type i) { return GetField<3>()[i]; }
    void         clear_child(size_type i) { SanitizerPoisonObject(&mutable_child(i)); }
    void         set_child(size_type i, btree_node* c) {
        SanitizerUnpoisonObject(&mutable_child(i));
        mutable_child(i) = c;
        c->set_position((field_type)i);
    }
#if defined(__GNUC__) || defined(__clang__)
    #pragma GCC diagnostic pop
#endif
    void init_child(int i, btree_node* c) {
        set_child(i, c);
        c->set_parent(this);
    }

    // Returns the position of the first value whose key is not less than k.
    // ----------------------------------------------------------------------
    template<typename K>
    SearchResult<int, is_key_compare_to::value> lower_bound(const K& k, const key_compare& comp) const {
        return use_linear_search::value ? linear_search(k, comp) : binary_search(k, comp);
    }
    // Returns the position of the first value whose key is greater than k.
    // --------------------------------------------------------------------
    template<typename K>
    int upper_bound(const K& k, const key_compare& comp) const {
        auto upper_compare = upper_bound_adapter<key_compare>(comp);
        return use_linear_search::value ? linear_search(k, upper_compare).value : binary_search(k, upper_compare).value;
    }

    template<typename K, typename Compare>
    SearchResult<int, btree_is_key_compare_to<Compare, key_type>::value> linear_search(const K&       k,
                                                                                       const Compare& comp) const {
        return linear_search_impl(k, 0, count(), comp, btree_is_key_compare_to<Compare, key_type>());
    }

    template<typename K, typename Compare>
    SearchResult<int, btree_is_key_compare_to<Compare, key_type>::value> binary_search(const K&       k,
                                                                                       const Compare& comp) const {
        return binary_search_impl(k, 0, count(), comp, btree_is_key_compare_to<Compare, key_type>());
    }

    // Returns the position of the first value whose key is not less than k using
    // linear search performed using plain compare.
    // --------------------------------------------------------------------------
    template<typename K, typename Compare>
    SearchResult<int, false> linear_search_impl(const K&       k,
                                                int            s,
                                                const int      e,
                                                const Compare& comp,
                                                std::false_type /* IsCompareTo */) const {
        while (s < e) {
            if (!comp(key(s), k)) {
                break;
            }
            ++s;
        }
        return { s };
    }

    // Returns the position of the first value whose key is not less than k using
    // linear search performed using compare-to.
    // --------------------------------------------------------------------------
    template<typename K, typename Compare>
    SearchResult<int, true> linear_search_impl(const K&       k,
                                               int            s,
                                               const int      e,
                                               const Compare& comp,
                                               std::true_type /* IsCompareTo */) const {
        while (s < e) {
            const gtl::weak_ordering c = comp(key(s), k);
            if (c == 0) {
                return { s, MatchKind::kEq };
            } else if (c > 0) {
                break;
            }
            ++s;
        }
        return { s, MatchKind::kNe };
    }

    // Returns the position of the first value whose key is not less than k using
    // binary search performed using plain compare.
    // --------------------------------------------------------------------------
    template<typename K, typename Compare>
    SearchResult<int, false> binary_search_impl(const K&       k,
                                                int            s,
                                                int            e,
                                                const Compare& comp,
                                                std::false_type /* IsCompareTo */) const {
        while (s != e) {
            const int mid = (s + e) >> 1;
            if (comp(key(mid), k)) {
                s = mid + 1;
            } else {
                e = mid;
            }
        }
        return { s };
    }

    // Returns the position of the first value whose key is not less than k using
    // binary search performed using compare-to.
    // --------------------------------------------------------------------------
    template<typename K, typename CompareTo>
    SearchResult<int, true> binary_search_impl(const K&         k,
                                               int              s,
                                               int              e,
                                               const CompareTo& comp,
                                               std::true_type /* IsCompareTo */) const {
        if (is_multi_container::value) {
            MatchKind exact_match = MatchKind::kNe;
            while (s != e) {
                const int                mid = (s + e) >> 1;
                const gtl::weak_ordering c   = comp(key(mid), k);
                if (c < 0) {
                    s = mid + 1;
                } else {
                    e = mid;
                    if (c == 0) {
                        // Need to return the first value whose key is not less than k,
                        // which requires continuing the binary search if this is a
                        // multi-container.
                        // ------------------------------------------------------------
                        exact_match = MatchKind::kEq;
                    }
                }
            }
            return { s, exact_match };
        } else { // Not a multi-container.
            while (s != e) {
                const int                mid = (s + e) >> 1;
                const gtl::weak_ordering c   = comp(key(mid), k);
                if (c < 0) {
                    s = mid + 1;
                } else if (c > 0) {
                    e = mid;
                } else {
                    return { mid, MatchKind::kEq };
                }
            }
            return { s, MatchKind::kNe };
        }
    }

    // Emplaces a value at position i, shifting all existing values and
    // children at positions >= i to the right by 1.
    // ----------------------------------------------------------------
    template<typename... Args>
    void emplace_value(size_type i, allocator_type* alloc, Args&&... args);

    // Removes the value at position i, shifting all existing values and children
    // at positions > i to the left by 1.
    // --------------------------------------------------------------------------
    void remove_value(int i, allocator_type* alloc);

    // Removes the values at positions [i, i + to_erase), shifting all values
    // after that range to the left by to_erase. Does not change children at all.
    // --------------------------------------------------------------------------
    void remove_values_ignore_children(int i, size_type to_erase, allocator_type* alloc);

    // Rebalances a node with its right sibling.
    // -----------------------------------------
    void rebalance_right_to_left(int to_move, btree_node* right, allocator_type* alloc);
    void rebalance_left_to_right(int to_move, btree_node* right, allocator_type* alloc);

    // Splits a node, moving a portion of the node's values to its right sibling.
    // --------------------------------------------------------------------------
    void split(int insert_position, btree_node* dest, allocator_type* alloc);

    // Merges a node with its right sibling, moving all of the values and the
    // delimiting key in the parent node onto itself.
    // ----------------------------------------------------------------------
    void merge(btree_node* sibling, allocator_type* alloc);

    // Swap the contents of "this" and "src".
    // --------------------------------------
    void swap(btree_node* src, allocator_type* alloc);

    // Node allocation/deletion routines.
    // ----------------------------------
    static btree_node* init_leaf(btree_node* n, btree_node* parent, int max_cnt) {
        n->set_parent(parent);
        n->set_position(0);
        n->set_start(0);
        n->set_count(0);
        n->set_max_count((field_type)max_cnt);
        SanitizerPoisonMemoryRegion(n->slot(0), max_cnt * sizeof(slot_type));
        return n;
    }

    static btree_node* init_internal(btree_node* n, btree_node* parent) {
        init_leaf(n, parent, kNodeValues);
        // Set `max_count` to a sentinel value to indicate that this node is
        // internal.
        n->set_max_count(kInternalNodeMaxCount);
        SanitizerPoisonMemoryRegion(&n->mutable_child(0), (kNodeValues + 1) * sizeof(btree_node*));
        return n;
    }

    void destroy(allocator_type* alloc) {
        for (int i = 0; i < count(); ++i) {
            value_destroy(i, alloc);
        }
    }

public:
    // Exposed only for tests.
    // -----------------------
    static bool testonly_uses_linear_node_search() { return use_linear_search::value; }

private:
    template<typename... Args>
    void value_init(const size_type i, allocator_type* alloc, Args&&... args) {
        SanitizerUnpoisonObject(slot(i));
        params_type::construct(alloc, slot(i), std::forward<Args>(args)...);
    }
    void value_destroy(const size_type i, allocator_type* alloc) {
        params_type::destroy(alloc, slot(i));
        SanitizerPoisonObject(slot(i));
    }

    // Move n values starting at value i in this node into the values starting at
    // value j in node x.
    // --------------------------------------------------------------------------
    void uninitialized_move_n(const size_type n,
                              const size_type i,
                              const size_type j,
                              btree_node*     x,
                              allocator_type* alloc) {
        SanitizerUnpoisonMemoryRegion(x->slot(j), n * sizeof(slot_type));
        for (slot_type *src = slot(i), *end = src + n, *dest = x->slot(j); src != end; ++src, ++dest) {
            params_type::construct(alloc, dest, src);
        }
    }

    // Destroys a range of n values, starting at index i.
    // --------------------------------------------------
    void value_destroy_n(const size_type i, const size_type n, allocator_type* alloc) {
        for (size_type j = 0; j < n; ++j) {
            value_destroy(i + j, alloc);
        }
    }

    template<typename P>
    friend class btree;

    template<typename N, typename R, typename P>
    friend struct btree_iterator;

    friend class BtreeNodePeer;
};

template<typename Node, typename Reference, typename Pointer>
struct btree_iterator {
private:
    using key_type    = typename Node::key_type;
    using size_type   = typename Node::size_type;
    using params_type = typename Node::params_type;

    using node_type        = Node;
    using normal_node      = typename std::remove_const<Node>::type;
    using const_node       = const Node;
    using normal_pointer   = typename params_type::pointer;
    using normal_reference = typename params_type::reference;
    using const_pointer    = typename params_type::const_pointer;
    using const_reference  = typename params_type::const_reference;
    using slot_type        = typename params_type::slot_type;

    using iterator       = btree_iterator<normal_node, normal_reference, normal_pointer>;
    using const_iterator = btree_iterator<const_node, const_reference, const_pointer>;

public:
    // These aliases are public for std::iterator_traits.
    // --------------------------------------------------
    using difference_type   = typename Node::difference_type;
    using value_type        = typename params_type::value_type;
    using pointer           = Pointer;
    using reference         = Reference;
    using iterator_category = std::bidirectional_iterator_tag;

    btree_iterator()
        : node(nullptr)
        , position(-1) {}
    btree_iterator(Node* n, int p)
        : node(n)
        , position(p) {}

    // NOTE: this SFINAE allows for implicit conversions from iterator to
    // const_iterator, but it specifically avoids defining copy constructors so
    // that btree_iterator can be trivially copyable. This is for performance and
    // binary size reasons.
    // --------------------------------------------------------------------------
    template<typename N,
             typename R,
             typename P,
             std::enable_if_t<std::is_same_v<btree_iterator<N, R, P>, iterator> &&
                                  std::is_same_v<btree_iterator, const_iterator>,
                              int> = 0>
    btree_iterator(const btree_iterator<N, R, P>& x) // NOLINT
        : node(x.node)
        , position(x.position) {}

private:
    // This SFINAE allows explicit conversions from const_iterator to
    // iterator, but also avoids defining a copy constructor.
    // NOTE: the const_cast is safe because this constructor is only called by
    // non-const methods and the container owns the nodes.
    // -----------------------------------------------------------------------
    template<typename N,
             typename R,
             typename P,
             std::enable_if_t<std::is_same_v<btree_iterator<N, R, P>, const_iterator> &&
                                  std::is_same_v<btree_iterator, iterator>,
                              int> = 0>
    explicit btree_iterator(const btree_iterator<N, R, P>& x)
        : node(const_cast<node_type*>(x.node))
        , position(x.position) {}

    // Increment/decrement the iterator.
    // ---------------------------------
    void increment() {
        if (node->leaf() && ++position < node->count()) {
            return;
        }
        increment_slow();
    }
    void increment_slow();

    void decrement() {
        if (node->leaf() && --position >= 0) {
            return;
        }
        decrement_slow();
    }
    void decrement_slow();

public:
    bool operator==(const const_iterator& x) const { return node == x.node && position == x.position; }
    bool operator!=(const const_iterator& x) const { return !(*this == x); }

    bool operator==(const iterator& x) const { return node == x.node && position == x.position; }
    bool operator!=(const iterator& x) const { return !(*this == x); }

    // Accessors for the key/value the iterator is pointing at.
    // --------------------------------------------------------
    reference operator*() const { return node->value(position); }
    pointer   operator->() const { return &node->value(position); }

    btree_iterator& operator++() {
        increment();
        return *this;
    }
    btree_iterator& operator--() {
        decrement();
        return *this;
    }
    btree_iterator operator++(int) {
        btree_iterator tmp = *this;
        ++*this;
        return tmp;
    }
    btree_iterator operator--(int) {
        btree_iterator tmp = *this;
        --*this;
        return tmp;
    }

private:
    template<typename Params>
    friend class btree;

    template<typename Tree>
    friend class btree_container;

    template<typename Tree>
    friend class btree_set_container;

    template<typename Tree>
    friend class btree_map_container;

    template<typename Tree>
    friend class btree_multiset_container;

    template<typename N, typename R, typename P>
    friend struct btree_iterator;

    template<typename TreeType, typename CheckerType>
    friend class base_checker;

    const key_type& key() const { return node->key(position); }
    slot_type*      slot() { return node->slot(position); }

    // The node in the tree the iterator is pointing at.
    // -------------------------------------------------
    Node* node;

    // The position within the node of the tree the iterator is pointing at.
    // TODO(ezb): make this a field_type
    // ----------------------------------------------------------------------
    int position;
};

template<typename Params>
class btree {
    using node_type         = btree_node<Params>;
    using is_key_compare_to = typename Params::is_key_compare_to;

    // We use a static empty node for the root/leftmost/rightmost of empty btrees
    // in order to avoid branching in begin()/end().
    // --------------------------------------------------------------------------
    struct alignas(node_type::Alignment()) EmptyNodeType : node_type {
        using field_type = typename node_type::field_type;
        node_type* parent;
        field_type position = 0;
        field_type start    = 0;
        field_type count    = 0;
        // max_count must be != kInternalNodeMaxCount (so that this node is regarded
        // as a leaf node). max_count() is never called when the tree is empty.
        field_type max_count = node_type::kInternalNodeMaxCount + 1;

#ifdef _MSC_VER
        // MSVC has constexpr code generations bugs here.
        EmptyNodeType()
            : parent(this) {}
#else
        constexpr EmptyNodeType(node_type* p)
            : parent(p) {}
#endif
    };

    static node_type* EmptyNode() {
#ifdef _MSC_VER
        static EmptyNodeType empty_node;
        // This assert fails on some other construction methods.
        assert(empty_node.parent == &empty_node);
        return &empty_node;
#else
        static constexpr EmptyNodeType empty_node(const_cast<EmptyNodeType*>(&empty_node));
        return const_cast<EmptyNodeType*>(&empty_node);
#endif
    }

    enum {
        kNodeValues    = node_type::kNodeValues,
        kMinNodeValues = kNodeValues / 2,
    };

    struct node_stats {
        using size_type = typename Params::size_type;

        node_stats(size_type l, size_type i)
            : leaf_nodes(l)
            , internal_nodes(i) {}

        node_stats& operator+=(const node_stats& x) {
            leaf_nodes += x.leaf_nodes;
            internal_nodes += x.internal_nodes;
            return *this;
        }

        size_type leaf_nodes;
        size_type internal_nodes;
    };

public:
    using key_type               = typename Params::key_type;
    using value_type             = typename Params::value_type;
    using size_type              = typename Params::size_type;
    using difference_type        = typename Params::difference_type;
    using key_compare            = typename Params::key_compare;
    using value_compare          = typename Params::value_compare;
    using allocator_type         = typename Params::allocator_type;
    using reference              = typename Params::reference;
    using const_reference        = typename Params::const_reference;
    using pointer                = typename Params::pointer;
    using const_pointer          = typename Params::const_pointer;
    using iterator               = btree_iterator<node_type, reference, pointer>;
    using const_iterator         = typename iterator::const_iterator;
    using reverse_iterator       = std::reverse_iterator<iterator>;
    using const_reverse_iterator = std::reverse_iterator<const_iterator>;
    using node_handle_type       = node_handle<Params, Params, allocator_type>;

    // Internal types made public for use by btree_container types.
    // ------------------------------------------------------------
    using params_type = Params;
    using slot_type   = typename Params::slot_type;

private:
    // For use in copy_or_move_values_in_order.
    // ----------------------------------------
    const value_type& maybe_move_from_iterator(const_iterator x) { return *x; }
    value_type&&      maybe_move_from_iterator(iterator x) { return std::move(*x); }

    // Copies or moves (depending on the template parameter) the values in
    // x into this btree in their order in x. This btree must be empty before this
    // method is called. This method is used in copy construction, copy
    // assignment, and move assignment.
    // --------------------------------------------------------------------------
    template<typename Btree>
    void copy_or_move_values_in_order(Btree* x);

    // Validates that various assumptions/requirements are true at compile time.
    // -------------------------------------------------------------------------
    constexpr static bool static_assert_validation();

public:
    btree(const key_compare& comp, const allocator_type& alloc);

    btree(const btree& x);

    btree(btree&& x) noexcept
        : root_(std::move(x.root_))
        , rightmost_(std::exchange(x.rightmost_, EmptyNode()))
        , size_(std::exchange(x.size_, 0)) {
        x.mutable_root() = EmptyNode();
    }

    ~btree() {
        // Put static_asserts in destructor to avoid triggering them before the type
        // is complete.
        // -------------------------------------------------------------------------
        static_assert(static_assert_validation(), "This call must be elided.");
        clear();
    }

    // Assign the contents of x to *this.
    // ----------------------------------
    btree& operator=(const btree& x);
    btree& operator=(btree&& x) noexcept;

    iterator               begin() { return iterator(leftmost(), 0); }
    const_iterator         begin() const { return const_iterator(leftmost(), 0); }
    iterator               end() { return iterator(rightmost_, rightmost_->count()); }
    const_iterator         end() const { return const_iterator(rightmost_, rightmost_->count()); }
    reverse_iterator       rbegin() { return reverse_iterator(end()); }
    const_reverse_iterator rbegin() const { return const_reverse_iterator(end()); }
    reverse_iterator       rend() { return reverse_iterator(begin()); }
    const_reverse_iterator rend() const { return const_reverse_iterator(begin()); }

    // Finds the first element whose key is not less than key.
    // -------------------------------------------------------
    template<typename K>
    iterator lower_bound(const K& key) {
        return internal_end(internal_lower_bound(key));
    }
    template<typename K>
    const_iterator lower_bound(const K& key) const {
        return internal_end(internal_lower_bound(key));
    }

    // Finds the first element whose key is greater than key.
    // ------------------------------------------------------
    template<typename K>
    iterator upper_bound(const K& key) {
        return internal_end(internal_upper_bound(key));
    }
    template<typename K>
    const_iterator upper_bound(const K& key) const {
        return internal_end(internal_upper_bound(key));
    }

    // Finds the range of values which compare equal to key. The first member of
    // the returned pair is equal to lower_bound(key). The second member pair of
    // the pair is equal to upper_bound(key).
    // -------------------------------------------------------------------------
    template<typename K>
    std::pair<iterator, iterator> equal_range(const K& key) {
        return { lower_bound(key), upper_bound(key) };
    }
    template<typename K>
    std::pair<const_iterator, const_iterator> equal_range(const K& key) const {
        return { lower_bound(key), upper_bound(key) };
    }

    // Inserts a value into the btree only if it does not already exist. The
    // boolean return value indicates whether insertion succeeded or failed.
    // Requirement: if `key` already exists in the btree, does not consume `args`.
    // Requirement: `key` is never referenced after consuming `args`.
    // ---------------------------------------------------------------------------
    template<typename... Args>
    std::pair<iterator, bool> insert_unique(const key_type& key, Args&&... args);

    // Inserts with hint. Checks to see if the value should be placed immediately
    // before `position` in the tree. If so, then the insertion will take
    // amortized constant time. If not, the insertion will take amortized
    // logarithmic time as if a call to insert_unique() were made.
    // Requirement: if `key` already exists in the btree, does not consume `args`.
    // Requirement: `key` is never referenced after consuming `args`.
    // ---------------------------------------------------------------------------
    template<typename... Args>
    std::pair<iterator, bool> insert_hint_unique(iterator position, const key_type& key, Args&&... args);

    // Insert a range of values into the btree.
    // ----------------------------------------
    template<typename InputIterator>
    void insert_iterator_unique(InputIterator b, InputIterator e);

    // Inserts a value into the btree.
    // -------------------------------
    template<typename ValueType>
    iterator insert_multi(const key_type& key, ValueType&& v);

    // Inserts a value into the btree.
    // -------------------------------
    template<typename ValueType>
    iterator insert_multi(ValueType&& v) {
        return insert_multi(params_type::key(v), std::forward<ValueType>(v));
    }

    // Insert with hint. Check to see if the value should be placed immediately
    // before position in the tree. If it does, then the insertion will take
    // amortized constant time. If not, the insertion will take amortized
    // logarithmic time as if a call to insert_multi(v) were made.
    // ------------------------------------------------------------------------
    template<typename ValueType>
    iterator insert_hint_multi(iterator position, ValueType&& v);

    // Insert a range of values into the btree.
    // ----------------------------------------
    template<typename InputIterator>
    void insert_iterator_multi(InputIterator b, InputIterator e);

    // Erase the specified iterator from the btree. The iterator must be valid
    // (i.e. not equal to end()).  Return an iterator pointing to the node after
    // the one that was erased (or end() if none exists).
    // Requirement: does not read the value at `*iter`.
    // ------------------------------------------------------------------------
    iterator erase(iterator iter);

    // Erases range. Returns the number of keys erased and an iterator pointing
    // to the element after the last erased element.
    // ------------------------------------------------------------------------
    std::pair<size_type, iterator> erase(iterator begin, iterator end);

    // Erases the specified key from the btree. Returns 1 if an element was
    // erased and 0 otherwise.
    // --------------------------------------------------------------------
    template<typename K>
    size_type erase_unique(const K& key);

    // Erases all of the entries matching the specified key from the
    // btree. Returns the number of elements erased.
    // -------------------------------------------------------------
    template<typename K>
    size_type erase_multi(const K& key);

    // Finds the iterator corresponding to a key or returns end() if the key is
    // not present.
    // ------------------------------------------------------------------------
    template<typename K>
    iterator find(const K& key) {
        return internal_end(internal_find(key));
    }
    template<typename K>
    const_iterator find(const K& key) const {
        return internal_end(internal_find(key));
    }

    // Returns a count of the number of times the key appears in the btree.
    // --------------------------------------------------------------------
    template<typename K>
    size_type count_unique(const K& key) const {
        const iterator beg = internal_find(key);
        if (beg.node == nullptr) {
            // The key doesn't exist in the tree.
            return 0;
        }
        return 1;
    }

    // Returns a count of the number of times the key appears in the btree.
    // --------------------------------------------------------------------
    template<typename K>
    size_type count_multi(const K& key) const {
        const auto range = equal_range(key);
        return std::distance(range.first, range.second);
    }

    // Clear the btree, deleting all of the values it contains.
    void clear();

    // Swap the contents of *this and x.
    // ---------------------------------
    void swap(btree& x);

    const key_compare& key_comp() const noexcept { return std::get<0>(root_); }
    template<typename K, typename LK>
    bool compare_keys(const K& x, const LK& y) const {
        return compare_internal::compare_result_as_less_than(key_comp()(x, y));
    }

    value_compare value_comp() const { return value_compare(key_comp()); }

    // Verifies the structure of the btree.
    // ------------------------------------
    void verify() const;

    // Size routines.
    // --------------
    size_type size() const { return size_; }
    size_type max_size() const { return (std::numeric_limits<size_type>::max)(); }
    bool      empty() const { return size_ == 0; }

    // The height of the btree. An empty tree will have height 0.
    // ----------------------------------------------------------
    size_type height() const {
        size_type h = 0;
        if (!empty()) {
            // Count the length of the chain from the leftmost node up to the
            // root. We actually count from the root back around to the level below
            // the root, but the calculation is the same because of the circularity
            // of that traversal.
            // ----------------------------------------------------------------------
            const node_type* n = root();
            do {
                ++h;
                n = n->parent();
            } while (n != root());
        }
        return h;
    }

    // The number of internal, leaf and total nodes used by the btree.
    // ---------------------------------------------------------------
    size_type leaf_nodes() const { return internal_stats(root()).leaf_nodes; }
    size_type internal_nodes() const { return internal_stats(root()).internal_nodes; }
    size_type nodes() const {
        node_stats stats = internal_stats(root());
        return stats.leaf_nodes + stats.internal_nodes;
    }

    // The total number of bytes used by the btree.
    // --------------------------------------------
    size_type bytes_used() const {
        node_stats stats = internal_stats(root());
        if (stats.leaf_nodes == 1 && stats.internal_nodes == 0) {
            return sizeof(*this) + node_type::LeafSize(root()->max_count());
        } else {
            return sizeof(*this) + stats.leaf_nodes * node_type::LeafSize() +
                   stats.internal_nodes * node_type::InternalSize();
        }
    }

    // The average number of bytes used per value stored in the btree.
    // ---------------------------------------------------------------
    static double average_bytes_per_value() {
        // Returns the number of bytes per value on a leaf node that is 75%
        // full. Experimentally, this matches up nicely with the computed number of
        // bytes per value in trees that had their values inserted in random order.
        // ------------------------------------------------------------------------
        return node_type::LeafSize() / (kNodeValues * 0.75);
    }

    // The fullness of the btree. Computed as the number of elements in the btree
    // divided by the maximum number of elements a tree with the current number
    // of nodes could hold. A value of 1 indicates perfect space
    // utilization. Smaller values indicate space wastage.
    // Returns 0 for empty trees.
    // --------------------------------------------------------------------------
    double fullness() const {
        if (empty())
            return 0.0;
        return static_cast<double>(size()) / (nodes() * kNodeValues);
    }

    // The overhead of the btree structure in bytes per node. Computed as the
    // total number of bytes used by the btree minus the number of bytes used for
    // storing elements divided by the number of elements.
    // Returns 0 for empty trees.
    // --------------------------------------------------------------------------
    double overhead() const {
        if (empty())
            return 0.0;
        return (bytes_used() - size() * sizeof(value_type)) / static_cast<double>(size());
    }

    // The allocator used by the btree.
    // --------------------------------
    allocator_type get_allocator() const { return allocator(); }

private:
    // Internal accessor routines.
    // ---------------------------
    node_type*       root() { return std::get<2>(root_); }
    const node_type* root() const { return std::get<2>(root_); }
    node_type*&      mutable_root() noexcept { return std::get<2>(root_); }
    key_compare*     mutable_key_comp() noexcept { return &std::get<0>(root_); }

    // The leftmost node is stored as the parent of the root node.
    // -----------------------------------------------------------
    node_type*       leftmost() { return root()->parent(); }
    const node_type* leftmost() const { return root()->parent(); }

    // Allocator routines.
    // -------------------
    allocator_type*       mutable_allocator() noexcept { return &std::get<1>(root_); }
    const allocator_type& allocator() const noexcept { return std::get<1>(root_); }

    // Allocates a correctly aligned node of at least size bytes using the
    // allocator.
    // -------------------------------------------------------------------
    node_type* allocate(const size_type sz) {
        return reinterpret_cast<node_type*>(Allocate<node_type::Alignment()>(mutable_allocator(), (size_t)sz));
    }

    // Node creation/deletion routines.
    // --------------------------------
    node_type* new_internal_node(node_type* parent) {
        node_type* p = allocate(node_type::InternalSize());
        return node_type::init_internal(p, parent);
    }
    node_type* new_leaf_node(node_type* parent) {
        node_type* p = allocate(node_type::LeafSize());
        return node_type::init_leaf(p, parent, kNodeValues);
    }
    node_type* new_leaf_root_node(const int max_count) {
        node_type* p = allocate(node_type::LeafSize(max_count));
        return node_type::init_leaf(p, p, max_count);
    }

    // Deletion helper routines.
    // -------------------------
    void     erase_same_node(iterator begin, iterator end);
    iterator erase_from_leaf_node(iterator begin, size_type to_erase);
    iterator rebalance_after_delete(iterator iter);

    // Deallocates a node of a certain size in bytes using the allocator.
    // ------------------------------------------------------------------
    void deallocate(const size_type sz, node_type* node) {
        Deallocate<node_type::Alignment()>(mutable_allocator(), node, (size_t)sz);
    }

    void delete_internal_node(node_type* node) {
        node->destroy(mutable_allocator());
        deallocate(node_type::InternalSize(), node);
    }
    void delete_leaf_node(node_type* node) {
        node->destroy(mutable_allocator());
        deallocate(node_type::LeafSize(node->max_count()), node);
    }

    // Rebalances or splits the node iter points to.
    // ---------------------------------------------
    void rebalance_or_split(iterator* iter);

    // Merges the values of left, right and the delimiting key on their parent
    // onto left, removing the delimiting key and deleting right.
    // ----------------------------------------------------------
    void merge_nodes(node_type* left, node_type* right);

    // Tries to merge node with its left or right sibling, and failing that,
    // rebalance with its left or right sibling. Returns true if a merge
    // occurred, at which point it is no longer valid to access node. Returns
    // false if no merging took place.
    // ----------------------------------------------------------------------
    bool try_merge_or_rebalance(iterator* iter);

    // Tries to shrink the height of the tree by 1.
    // --------------------------------------------
    void try_shrink();

    iterator       internal_end(iterator iter) { return iter.node != nullptr ? iter : end(); }
    const_iterator internal_end(const_iterator iter) const { return iter.node != nullptr ? iter : end(); }

    // Emplaces a value into the btree immediately before iter. Requires that
    // key(v) <= iter.key() and (--iter).key() <= key(v).
    // ----------------------------------------------------------------------
    template<typename... Args>
    iterator internal_emplace(iterator iter, Args&&... args);

    // Returns an iterator pointing to the first value >= the value "iter" is
    // pointing at. Note that "iter" might be pointing to an invalid location as
    // iter.position == iter.node->count(). This routine simply moves iter up in
    // the tree to a valid location.
    // Requires: iter.node is non-null.
    // -------------------------------------------------------------------------
    template<typename IterType>
    static IterType internal_last(IterType iter);

    // Returns an iterator pointing to the leaf position at which key would
    // reside in the tree. We provide 2 versions of internal_locate. The first
    // version uses a less-than comparator and is incapable of distinguishing when
    // there is an exact match. The second version is for the key-compare-to
    // specialization and distinguishes exact matches. The key-compare-to
    // specialization allows the caller to avoid a subsequent comparison to
    // determine if an exact match was made, which is important for keys with
    // expensive comparison, such as strings.
    // --------------------------------------------------------------------------
    template<typename K>
    SearchResult<iterator, is_key_compare_to::value> internal_locate(const K& key) const;

    template<typename K>
    SearchResult<iterator, false> internal_locate_impl(const K& key, std::false_type /* IsCompareTo */) const;

    template<typename K>
    SearchResult<iterator, true> internal_locate_impl(const K& key, std::true_type /* IsCompareTo */) const;

    // Internal routine which implements lower_bound()
    // -----------------------------------------------.
    template<typename K>
    iterator internal_lower_bound(const K& key) const;

    // Internal routine which implements upper_bound().
    // ------------------------------------------------
    template<typename K>
    iterator internal_upper_bound(const K& key) const;

    // Internal routine which implements find()
    // ----------------------------------------.
    template<typename K>
    iterator internal_find(const K& key) const;

    // Deletes a node and all of its children.
    // ---------------------------------------
    void internal_clear(node_type* node);

    // Verifies the tree structure of node.
    // ------------------------------------
    size_type internal_verify(const node_type* node, const key_type* lo, const key_type* hi) const;

    node_stats internal_stats(const node_type* node) const {
        // The root can be a static empty node.
        // ------------------------------------
        if (node == nullptr || (node == root() && empty())) {
            return node_stats(0, 0);
        }
        if (node->leaf()) {
            return node_stats(1, 0);
        }
        node_stats res(0, 1);
        for (int i = 0; i <= node->count(); ++i) {
            res += internal_stats(node->child(i));
        }
        return res;
    }

public:
    // Exposed only for tests.
    // -----------------------
    static bool testonly_uses_linear_node_search() { return node_type::testonly_uses_linear_node_search(); }

private:
    std::tuple<key_compare, allocator_type, node_type*> root_;

    // A pointer to the rightmost node. Note that the leftmost node is stored as
    // the root's parent.
    // -------------------------------------------------------------------------
    node_type* rightmost_;

    size_type size_;
};

////
// btree_node methods
// ----------------------------------------------------------------------
template<typename P>
template<typename... Args>
inline void btree_node<P>::emplace_value(const size_type i, allocator_type* alloc, Args&&... args) {
    assert(i <= count());
    // Shift old values to create space for new value and then construct it in
    // place.
    // -----------------------------------------------------------------------
    if (i < count()) {
        value_init(count(), alloc, slot(count() - 1));
        for (size_type j = count() - 1; j > i; --j)
            params_type::move(alloc, slot(j - 1), slot(j));
        value_destroy(i, alloc);
    }
    value_init(i, alloc, std::forward<Args>(args)...);
    set_count((field_type)(count() + 1));

    if (!leaf() && count() > i + 1) {
        for (int j = count(); j > (int)(i + 1); --j) {
            set_child(j, child(j - 1));
        }
        clear_child(i + 1);
    }
}

template<typename P>
inline void btree_node<P>::remove_value(const int i, allocator_type* alloc) {
    if (!leaf() && count() > i + 1) {
        assert(child(i + 1)->count() == 0);
        for (size_type j = i + 1; j < count(); ++j) {
            set_child(j, child(j + 1));
        }
        clear_child(count());
    }

    remove_values_ignore_children(i, /*to_erase=*/1, alloc);
}

template<typename P>
inline void btree_node<P>::remove_values_ignore_children(int i, size_type to_erase, allocator_type* alloc) {
    params_type::move(alloc, slot(i + to_erase), slot(count()), slot(i));
    value_destroy_n(count() - to_erase, to_erase, alloc);
    set_count((field_type)(count() - to_erase));
}

template<typename P>
void btree_node<P>::rebalance_right_to_left(const int to_move, btree_node* right, allocator_type* alloc) {
    assert(parent() == right->parent());
    assert(position() + 1 == right->position());
    assert(right->count() >= count());
    assert(to_move >= 1);
    assert(to_move <= right->count());

    // 1) Move the delimiting value in the parent to the left node.
    value_init(count(), alloc, parent()->slot(position()));

    // 2) Move the (to_move - 1) values from the right node to the left node.
    right->uninitialized_move_n(to_move - 1, 0, count() + 1, this, alloc);

    // 3) Move the new delimiting value to the parent from the right node.
    params_type::move(alloc, right->slot(to_move - 1), parent()->slot(position()));

    // 4) Shift the values in the right node to their correct position.
    params_type::move(alloc, right->slot(to_move), right->slot(right->count()), right->slot(0));

    // 5) Destroy the now-empty to_move entries in the right node.
    right->value_destroy_n(right->count() - to_move, to_move, alloc);

    if (!leaf()) {
        // Move the child pointers from the right to the left node.
        for (int i = 0; i < to_move; ++i) {
            init_child(count() + i + 1, right->child(i));
        }
        for (int i = 0; i <= right->count() - to_move; ++i) {
            assert(i + to_move <= right->max_count());
            right->init_child(i, right->child(i + to_move));
            right->clear_child(i + to_move);
        }
    }

    // Fixup the counts on the left and right nodes.
    set_count((field_type)(count() + to_move));
    right->set_count((field_type)(right->count() - to_move));
}

template<typename P>
void btree_node<P>::rebalance_left_to_right(const int to_move, btree_node* right, allocator_type* alloc) {
    assert(parent() == right->parent());
    assert(position() + 1 == right->position());
    assert(count() >= right->count());
    assert(to_move >= 1);
    assert(to_move <= count());

    // Values in the right node are shifted to the right to make room for the
    // new to_move values. Then, the delimiting value in the parent and the
    // other (to_move - 1) values in the left node are moved into the right node.
    // Lastly, a new delimiting value is moved from the left node into the
    // parent, and the remaining empty left node entries are destroyed.
    // -------------------------------------------------------------------------

    if (right->count() >= to_move) {
        // The original location of the right->count() values are sufficient to hold
        // the new to_move entries from the parent and left node.

        // 1) Shift existing values in the right node to their correct positions.
        // ----------------------------------------------------------------------
        right->uninitialized_move_n(to_move, right->count() - to_move, right->count(), right, alloc);
        if (right->count() > to_move) {
            for (slot_type *src  = right->slot(right->count() - to_move - 1),
                           *dest = right->slot(right->count() - 1),
                           *end  = right->slot(0);
                 src >= end;
                 --src, --dest)
            {
                params_type::move(alloc, src, dest);
            }
        }

        // 2) Move the delimiting value in the parent to the right node.
        // ----------------------------------------------------------------------
        params_type::move(alloc, parent()->slot(position()), right->slot(to_move - 1));

        // 3) Move the (to_move - 1) values from the left node to the right node.
        // ----------------------------------------------------------------------
        params_type::move(alloc, slot(count() - (to_move - 1)), slot(count()), right->slot(0));
    } else {
        // The right node does not have enough initialized space to hold the new
        // to_move entries, so part of them will move to uninitialized space.

        // 1) Shift existing values in the right node to their correct positions.
        // ----------------------------------------------------------------------
        right->uninitialized_move_n(right->count(), 0, to_move, right, alloc);

        // 2) Move the delimiting value in the parent to the right node.
        // ----------------------------------------------------------------------
        right->value_init(to_move - 1, alloc, parent()->slot(position()));

        // 3) Move the (to_move - 1) values from the left node to the right node.
        // ----------------------------------------------------------------------
        const size_type uninitialized_remaining = to_move - right->count() - 1;
        uninitialized_move_n(uninitialized_remaining, count() - uninitialized_remaining, right->count(), right, alloc);
        params_type::move(
            alloc, slot(count() - (to_move - 1)), slot(count() - uninitialized_remaining), right->slot(0));
    }

    // 4) Move the new delimiting value to the parent from the left node.
    // ------------------------------------------------------------------
    params_type::move(alloc, slot(count() - to_move), parent()->slot(position()));

    // 5) Destroy the now-empty to_move entries in the left node.
    // ----------------------------------------------------------
    value_destroy_n(count() - to_move, to_move, alloc);

    if (!leaf()) {
        // Move the child pointers from the left to the right node.
        // --------------------------------------------------------
        for (int i = right->count(); i >= 0; --i) {
            right->init_child(i + to_move, right->child(i));
            right->clear_child(i);
        }
        for (int i = 1; i <= to_move; ++i) {
            right->init_child(i - 1, child(count() - to_move + i));
            clear_child(count() - to_move + i);
        }
    }

    // Fixup the counts on the left and right nodes.
    // ---------------------------------------------
    set_count((field_type)(count() - to_move));
    right->set_count((field_type)(right->count() + to_move));
}

template<typename P>
void btree_node<P>::split(const int insert_position, btree_node* dest, allocator_type* alloc) {
    assert(dest->count() == 0);
    assert(max_count() == kNodeValues);

    // We bias the split based on the position being inserted. If we're
    // inserting at the beginning of the left node then bias the split to put
    // more values on the right node. If we're inserting at the end of the
    // right node then bias the split to put more values on the left node.
    // ----------------------------------------------------------------------
    if (insert_position == 0) {
        dest->set_count((field_type)(count() - 1));
    } else if (insert_position == kNodeValues) {
        dest->set_count(0);
    } else {
        dest->set_count((field_type)(count() / 2));
    }
    set_count((field_type)(count() - dest->count()));
    assert(count() >= 1);

    // Move values from the left sibling to the right sibling.
    // -------------------------------------------------------
    uninitialized_move_n(dest->count(), count(), 0, dest, alloc);

    // Destroy the now-empty entries in the left node.
    // -----------------------------------------------
    value_destroy_n(count(), dest->count(), alloc);

    // The split key is the largest value in the left sibling.
    // -------------------------------------------------------
    set_count((field_type)(count() - 1));
    parent()->emplace_value(position(), alloc, slot(count()));
    value_destroy(count(), alloc);
    parent()->init_child(position() + 1, dest);

    if (!leaf()) {
        for (int i = 0; i <= dest->count(); ++i) {
            assert(child(count() + i + 1) != nullptr);
            dest->init_child(i, child(count() + i + 1));
            clear_child(count() + i + 1);
        }
    }
}

template<typename P>
void btree_node<P>::merge(btree_node* src, allocator_type* alloc) {
    assert(parent() == src->parent());
    assert(position() + 1 == src->position());

    // Move the delimiting value to the left node.
    // -------------------------------------------
    value_init(count(), alloc, parent()->slot(position()));

    // Move the values from the right to the left node.
    // ------------------------------------------------
    src->uninitialized_move_n(src->count(), 0, count() + 1, this, alloc);

    // Destroy the now-empty entries in the right node.
    // ------------------------------------------------
    src->value_destroy_n(0, src->count(), alloc);

    if (!leaf()) {
        // Move the child pointers from the right to the left node.
        // --------------------------------------------------------
        for (int i = 0; i <= src->count(); ++i) {
            init_child(count() + i + 1, src->child(i));
            src->clear_child(i);
        }
    }

    // Fixup the counts on the src and dest nodes.
    // -------------------------------------------
    set_count((field_type)(1 + count() + src->count()));
    src->set_count(0);

    // Remove the value on the parent node.
    // ------------------------------------
    parent()->remove_value(position(), alloc);
}

template<typename P>
void btree_node<P>::swap(btree_node* x, allocator_type* alloc) {
    using std::swap;
    assert(leaf() == x->leaf());

    // Determine which is the smaller/larger node.
    // -------------------------------------------
    btree_node *smaller = this, *larger = x;
    if (smaller->count() > larger->count()) {
        swap(smaller, larger);
    }

    // Swap the values.
    // ----------------
    for (slot_type *a = smaller->slot(0), *b = larger->slot(0), *end = a + smaller->count(); a != end; ++a, ++b) {
        params_type::swap(alloc, a, b);
    }

    // Move values that can't be swapped.
    // ----------------------------------
    const size_type to_move = larger->count() - smaller->count();
    larger->uninitialized_move_n(to_move, smaller->count(), smaller->count(), smaller, alloc);
    larger->value_destroy_n(smaller->count(), to_move, alloc);

    if (!leaf()) {
        // Swap the child pointers.
        // ------------------------
        std::swap_ranges(
            &smaller->mutable_child(0), &smaller->mutable_child(smaller->count() + 1), &larger->mutable_child(0));

        // Update swapped children's parent pointers.
        // ------------------------------------------
        int i = 0;
        for (; i <= smaller->count(); ++i) {
            smaller->child(i)->set_parent(smaller);
            larger->child(i)->set_parent(larger);
        }

        // Move the child pointers that couldn't be swapped.
        // -------------------------------------------------
        for (; i <= larger->count(); ++i) {
            smaller->init_child(i, larger->child(i));
            larger->clear_child(i);
        }
    }

    // Swap the counts.
    // ----------------
    swap(mutable_count(), x->mutable_count());
}

////
// btree_iterator methods
// ----------------------------------------------------------------------
template<typename N, typename R, typename P>
void btree_iterator<N, R, P>::increment_slow() {
    if (node->leaf()) {
        assert(position >= node->count());
        btree_iterator save(*this);
        while (position == node->count() && !node->is_root()) {
            assert(node->parent()->child(node->position()) == node);
            position = node->position();
            node     = node->parent();
        }
        if (position == node->count()) {
            *this = save;
        }
    } else {
        assert(position < node->count());
        node = node->child(position + 1);
        while (!node->leaf()) {
            node = node->child(0);
        }
        position = 0;
    }
}

template<typename N, typename R, typename P>
void btree_iterator<N, R, P>::decrement_slow() {
    if (node->leaf()) {
        assert(position <= -1);
        btree_iterator save(*this);
        while (position < 0 && !node->is_root()) {
            assert(node->parent()->child(node->position()) == node);
            position = node->position() - 1;
            node     = node->parent();
        }
        if (position < 0) {
            *this = save;
        }
    } else {
        assert(position >= 0);
        node = node->child(position);
        while (!node->leaf()) {
            node = node->child(node->count());
        }
        position = node->count() - 1;
    }
}

////
// btree methods
// ----------------------------------------------------------------------
template<typename P>
template<typename Btree>
void btree<P>::copy_or_move_values_in_order(Btree* x) {
    static_assert(std::is_same_v<btree, Btree> || std::is_same_v<const btree, Btree>,
                  "Btree type must be same or const.");
    assert(empty());

    // We can avoid key comparisons because we know the order of the
    // values is the same order we'll store them in.
    // -------------------------------------------------------------
    auto iter = x->begin();
    if (iter == x->end())
        return;
    insert_multi(maybe_move_from_iterator(iter));
    ++iter;
    for (; iter != x->end(); ++iter) {
        // If the btree is not empty, we can just insert the new value at the end
        // of the tree.
        // ----------------------------------------------------------------------
        internal_emplace(end(), maybe_move_from_iterator(iter));
    }
}

template<typename P>
constexpr bool btree<P>::static_assert_validation() {
    static_assert(std::is_nothrow_copy_constructible_v<key_compare>,
                  "Key comparison must be nothrow copy constructible");
    static_assert(std::is_nothrow_copy_constructible_v<allocator_type>, "Allocator must be nothrow copy constructible");
    static_assert(std::is_trivially_copyable<iterator>::value, "iterator not trivially copyable.");

    // Note: We assert that kTargetValues, which is computed from
    // Params::kTargetNodeSize, must fit the node_type::field_type.
    // ------------------------------------------------------------
    static_assert(kNodeValues < (1 << (8 * sizeof(typename node_type::field_type))), "target node size too large");

    // Verify that key_compare returns an std::{weak,strong}_ordering or bool.
    // -----------------------------------------------------------------------
    using compare_result_type = std::invoke_result_t<key_compare, key_type, key_type>;
    static_assert(std::is_same_v<compare_result_type, bool> ||
                      std::is_convertible_v<compare_result_type, gtl::weak_ordering>,
                  "key comparison function must return std::{weak,strong}_ordering or bool.");

    // Test the assumption made in setting kNodeSlotSpace.
    // ----------------------------------------------------
    static_assert(node_type::MinimumOverhead() >= sizeof(void*) + 4, "node space assumption incorrect");

    return true;
}

template<typename P>
btree<P>::btree(const key_compare& comp, const allocator_type& alloc)
    : root_(comp, alloc, EmptyNode())
    , rightmost_(EmptyNode())
    , size_(0) {}

template<typename P>
btree<P>::btree(const btree& x)
    : btree(x.key_comp(), x.allocator()) {
    copy_or_move_values_in_order(&x);
}

template<typename P>
template<typename... Args>
auto btree<P>::insert_unique(const key_type& key, Args&&... args) -> std::pair<iterator, bool> {
    if (empty()) {
        mutable_root() = rightmost_ = new_leaf_root_node(1);
    }

    auto      res  = internal_locate(key);
    iterator& iter = res.value;

    if (res.HasMatch()) {
        if (res.IsEq()) {
            // The key already exists in the tree, do nothing.
            // -----------------------------------------------
            return { iter, false };
        }
    } else {
        iterator last = internal_last(iter);
        if (last.node && !compare_keys(key, last.key())) {
            // The key already exists in the tree, do nothing.
            return { last, false };
        }
    }
    return { internal_emplace(iter, std::forward<Args>(args)...), true };
}

template<typename P>
template<typename... Args>
inline auto btree<P>::insert_hint_unique(iterator position, const key_type& key, Args&&... args)
    -> std::pair<iterator, bool> {
    if (!empty()) {
        if (position == end() || compare_keys(key, position.key())) {
            iterator prev = position;
            if (position == begin() || compare_keys((--prev).key(), key)) {
                // prev.key() < key < position.key()
                // ---------------------------------
                return { internal_emplace(position, std::forward<Args>(args)...), true };
            }
        } else if (compare_keys(position.key(), key)) {
            ++position;
            if (position == end() || compare_keys(key, position.key())) {
                // {original `position`}.key() < key < {current `position`}.key()
                // --------------------------------------------------------------
                return { internal_emplace(position, std::forward<Args>(args)...), true };
            }
        } else {
            // position.key() == key
            // ---------------------
            return { position, false };
        }
    }
    return insert_unique(key, std::forward<Args>(args)...);
}

template<typename P>
template<typename InputIterator>
void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e) {
    for (; b != e; ++b) {
        insert_hint_unique(end(), params_type::key(*b), *b);
    }
}

template<typename P>
template<typename ValueType>
auto btree<P>::insert_multi(const key_type& key, ValueType&& v) -> iterator {
    if (empty()) {
        mutable_root() = rightmost_ = new_leaf_root_node(1);
    }

    iterator iter = internal_upper_bound(key);
    if (iter.node == nullptr) {
        iter = end();
    }
    return internal_emplace(iter, std::forward<ValueType>(v));
}

template<typename P>
template<typename ValueType>
auto btree<P>::insert_hint_multi(iterator position, ValueType&& v) -> iterator {
    if (!empty()) {
        const key_type& key = params_type::key(v);
        if (position == end() || !compare_keys(position.key(), key)) {
            iterator prev = position;
            if (position == begin() || !compare_keys(key, (--prev).key())) {
                // prev.key() <= key <= position.key()
                // -----------------------------------
                return internal_emplace(position, std::forward<ValueType>(v));
            }
        } else {
            iterator next = position;
            ++next;
            if (next == end() || !compare_keys(next.key(), key)) {
                // position.key() < key <= next.key()
                // ----------------------------------
                return internal_emplace(next, std::forward<ValueType>(v));
            }
        }
    }
    return insert_multi(std::forward<ValueType>(v));
}

template<typename P>
template<typename InputIterator>
void btree<P>::insert_iterator_multi(InputIterator b, InputIterator e) {
    for (; b != e; ++b) {
        insert_hint_multi(end(), *b);
    }
}

template<typename P>
auto btree<P>::operator=(const btree& x) -> btree& {
    if (this != &x) {
        clear();

        *mutable_key_comp() = x.key_comp();
        if (std::allocator_traits<allocator_type>::propagate_on_container_copy_assignment::value) {
            *mutable_allocator() = x.allocator();
        }

        copy_or_move_values_in_order(&x);
    }
    return *this;
}

template<typename P>
auto btree<P>::operator=(btree&& x) noexcept -> btree& {
    if (this != &x) {
        clear();

        using std::swap;
        if (std::allocator_traits<allocator_type>::propagate_on_container_copy_assignment::value) {
            // Note: `root_` also contains the allocator and the key comparator.
            swap(root_, x.root_);
            swap(rightmost_, x.rightmost_);
            swap(size_, x.size_);
        } else {
            if (allocator() == x.allocator()) {
                swap(mutable_root(), x.mutable_root());
                swap(*mutable_key_comp(), *x.mutable_key_comp());
                swap(rightmost_, x.rightmost_);
                swap(size_, x.size_);
            } else {
                // We aren't allowed to propagate the allocator and the allocator is
                // different so we can't take over its memory. We must move each element
                // individually. We need both `x` and `this` to have `x`s key comparator
                // while moving the values so we can't swap the key comparators.
                // ----------------------------------------------------------------------
                *mutable_key_comp() = x.key_comp();
                copy_or_move_values_in_order(&x);
            }
        }
    }
    return *this;
}

template<typename P>
auto btree<P>::erase(iterator iter) -> iterator {
    bool internal_delete = false;
    if (!iter.node->leaf()) {
        // Deletion of a value on an internal node. First, move the largest value
        // from our left child here, then delete that position (in remove_value()
        // below). We can get to the largest value from our left child by
        // decrementing iter.
        // ----------------------------------------------------------------------
        iterator internal_iter(iter);
        --iter;
        assert(iter.node->leaf());
        params_type::move(
            mutable_allocator(), iter.node->slot(iter.position), internal_iter.node->slot(internal_iter.position));
        internal_delete = true;
    }

    // Delete the key from the leaf.
    iter.node->remove_value(iter.position, mutable_allocator());
    --size_;

    // We want to return the next value after the one we just erased. If we
    // erased from an internal node (internal_delete == true), then the next
    // value is ++(++iter). If we erased from a leaf node (internal_delete ==
    // false) then the next value is ++iter. Note that ++iter may point to an
    // internal node and the value in the internal node may move to a leaf node
    // (iter.node) when rebalancing is performed at the leaf level.
    // ----------------------------------------------------------------------

    iterator res = rebalance_after_delete(iter);

    // If we erased from an internal node, advance the iterator.
    if (internal_delete) {
        ++res;
    }
    return res;
}

template<typename P>
auto btree<P>::rebalance_after_delete(iterator iter) -> iterator {
    // Merge/rebalance as we walk back up the tree.
    iterator res(iter);
    bool     first_iteration = true;
    for (;;) {
        if (iter.node == root()) {
            try_shrink();
            if (empty()) {
                return end();
            }
            break;
        }
        if (iter.node->count() >= kMinNodeValues) {
            break;
        }
        bool merged = try_merge_or_rebalance(&iter);
        // On the first iteration, we should update `res` with `iter` because `res`
        // may have been invalidated.
        // ------------------------------------------------------------------------
        if (first_iteration) {
            res             = iter;
            first_iteration = false;
        }
        if (!merged) {
            break;
        }
        iter.position = iter.node->position();
        iter.node     = iter.node->parent();
    }

    // Adjust our return value. If we're pointing at the end of a node, advance
    // the iterator.
    // ------------------------------------------------------------------------
    if (res.position == res.node->count()) {
        res.position = res.node->count() - 1;
        ++res;
    }

    return res;
}

template<typename P>
auto btree<P>::erase(iterator _begin, iterator _end) -> std::pair<size_type, iterator> {
    difference_type count = std::distance(_begin, _end);
    assert(count >= 0);

    if (count == 0) {
        return { 0, _begin };
    }

    if (count == (difference_type)size_) {
        clear();
        return { count, this->end() };
    }

    if (_begin.node == _end.node) {
        erase_same_node(_begin, _end);
        size_ -= count;
        return { count, rebalance_after_delete(_begin) };
    }

    const size_type target_size = size_ - count;
    while (size_ > target_size) {
        if (_begin.node->leaf()) {
            const size_type remaining_to_erase = size_ - target_size;
            const size_type remaining_in_node  = _begin.node->count() - _begin.position;
            _begin = erase_from_leaf_node(_begin, (std::min)(remaining_to_erase, remaining_in_node));
        } else {
            _begin = erase(_begin);
        }
    }
    return { count, _begin };
}

template<typename P>
void btree<P>::erase_same_node(iterator _begin, iterator _end) {
    assert(_begin.node == _end.node);
    assert(_end.position > _begin.position);

    node_type* node     = _begin.node;
    size_type  to_erase = _end.position - _begin.position;
    if (!node->leaf()) {
        // Delete all children between _begin and _end.
        // --------------------------------------------
        for (size_type i = 0; i < to_erase; ++i) {
            internal_clear(node->child(_begin.position + i + 1));
        }
        // Rotate children after _end into new positions.
        // ----------------------------------------------
        for (size_type i = _begin.position + to_erase + 1; i <= node->count(); ++i) {
            node->set_child(i - to_erase, node->child(i));
            node->clear_child(i);
        }
    }
    node->remove_values_ignore_children(_begin.position, to_erase, mutable_allocator());

    // ---------------------------------------------------------------------------
    // Do not need to update rightmost_, because
    // * either _end == this->end(), and therefore node == rightmost_, and still
    //   exists
    // * or _end != this->end(), and therefore rightmost_ hasn't been erased, since
    //   it wasn't covered in [_begin, _end)
    // ----------------------------------------------------------------------------
}

template<typename P>
auto btree<P>::erase_from_leaf_node(iterator _begin, size_type to_erase) -> iterator {
    node_type* node = _begin.node;
    assert(node->leaf());
    assert(node->count() > _begin.position);
    assert(_begin.position + to_erase <= node->count());

    node->remove_values_ignore_children(_begin.position, to_erase, mutable_allocator());

    size_ -= to_erase;

    return rebalance_after_delete(_begin);
}

template<typename P>
template<typename K>
auto btree<P>::erase_unique(const K& key) -> size_type {
    const iterator iter = internal_find(key);
    if (iter.node == nullptr) {
        // The key doesn't exist in the tree, return nothing done.
        // -------------------------------------------------------
        return 0;
    }
    erase(iter);
    return 1;
}

template<typename P>
template<typename K>
auto btree<P>::erase_multi(const K& key) -> size_type {
    const iterator _begin = internal_lower_bound(key);
    if (_begin.node == nullptr) {
        // The key doesn't exist in the tree, return nothing done.
        // -------------------------------------------------------
        return 0;
    }
    // Delete all of the keys between _begin and upper_bound(key).
    // -----------------------------------------------------------
    const iterator _end = internal_end(internal_upper_bound(key));
    return erase(_begin, _end).first;
}

template<typename P>
void btree<P>::clear() {
    if (!empty()) {
        internal_clear(root());
    }
    mutable_root() = EmptyNode();
    rightmost_     = EmptyNode();
    size_          = 0;
}

template<typename P>
void btree<P>::swap(btree& x) {
    using std::swap;
    if (std::allocator_traits<allocator_type>::propagate_on_container_swap::value) {
        // Note: `root_` also contains the allocator and the key comparator.
        // -----------------------------------------------------------------
        swap(root_, x.root_);
    } else {
        // It's undefined behavior if the allocators are unequal here.
        // -----------------------------------------------------------
        assert(allocator() == x.allocator());
        swap(mutable_root(), x.mutable_root());
        swap(*mutable_key_comp(), *x.mutable_key_comp());
    }
    swap(rightmost_, x.rightmost_);
    swap(size_, x.size_);
}

template<typename P>
void btree<P>::verify() const {
    assert(root() != nullptr);
    assert(leftmost() != nullptr);
    assert(rightmost_ != nullptr);
    assert(empty() || size() == internal_verify(root(), nullptr, nullptr));
    assert(leftmost() == (++const_iterator(root(), -1)).node);
    assert(rightmost_ == (--const_iterator(root(), root()->count())).node);
    assert(leftmost()->leaf());
    assert(rightmost_->leaf());
}

template<typename P>
void btree<P>::rebalance_or_split(iterator* iter) {
    node_type*& node            = iter->node;
    int&        insert_position = iter->position;
    assert(node->count() == node->max_count());
    assert(kNodeValues == node->max_count());

    // First try to make room on the node by rebalancing.
    // --------------------------------------------------
    node_type* parent = node->parent();
    if (node != root()) {
        if (node->position() > 0) {
            // Try rebalancing with our left sibling.
            // --------------------------------------
            node_type* left = parent->child(node->position() - 1);
            assert(left->max_count() == kNodeValues);
            if (left->count() < kNodeValues) {
                // We bias rebalancing based on the position being inserted. If we're
                // inserting at the end of the right node then we bias rebalancing to
                // fill up the left node.
                // ------------------------------------------------------------------
                int to_move = (kNodeValues - left->count()) / (1 + (insert_position < kNodeValues));
                to_move     = (std::max)(1, to_move);

                if (((insert_position - to_move) >= 0) || ((left->count() + to_move) < kNodeValues)) {
                    left->rebalance_right_to_left(to_move, node, mutable_allocator());

                    assert(node->max_count() - node->count() == to_move);
                    insert_position = insert_position - to_move;
                    if (insert_position < 0) {
                        insert_position = insert_position + left->count() + 1;
                        node            = left;
                    }

                    assert(node->count() < node->max_count());
                    return;
                }
            }
        }

        if (node->position() < parent->count()) {
            // Try rebalancing with our right sibling.
            // ---------------------------------------
            node_type* right = parent->child(node->position() + 1);
            assert(right->max_count() == kNodeValues);
            if (right->count() < kNodeValues) {
                // We bias rebalancing based on the position being inserted. If we're
                // inserting at the _beginning of the left node then we bias rebalancing
                // to fill up the right node.
                // ---------------------------------------------------------------------
                int to_move = (kNodeValues - right->count()) / (1 + (insert_position > 0));
                to_move     = (std::max)(1, to_move);

                if ((insert_position <= (node->count() - to_move)) || ((right->count() + to_move) < kNodeValues)) {
                    node->rebalance_left_to_right(to_move, right, mutable_allocator());

                    if (insert_position > node->count()) {
                        insert_position = insert_position - node->count() - 1;
                        node            = right;
                    }

                    assert(node->count() < node->max_count());
                    return;
                }
            }
        }

        // Rebalancing failed, make sure there is room on the parent node for a new
        // value.
        // ------------------------------------------------------------------------
        assert(parent->max_count() == kNodeValues);
        if (parent->count() == kNodeValues) {
            iterator parent_iter(node->parent(), node->position());
            rebalance_or_split(&parent_iter);
        }
    } else {
        // Rebalancing not possible because this is the root node.
        // Create a new root node and set the current root node as the child of the
        // new root.
        // ------------------------------------------------------------------------
        parent = new_internal_node(parent);
        parent->init_child(0, root());
        mutable_root() = parent;
        // If the former root was a leaf node, then it's now the rightmost node.
        // ---------------------------------------------------------------------
        assert(!parent->child(0)->leaf() || parent->child(0) == rightmost_);
    }

    // Split the node.
    // ---------------
    node_type* split_node;
    if (node->leaf()) {
        split_node = new_leaf_node(parent);
        node->split(insert_position, split_node, mutable_allocator());
        if (rightmost_ == node)
            rightmost_ = split_node;
    } else {
        split_node = new_internal_node(parent);
        node->split(insert_position, split_node, mutable_allocator());
    }

    if (insert_position > node->count()) {
        insert_position = insert_position - node->count() - 1;
        node            = split_node;
    }
}

template<typename P>
void btree<P>::merge_nodes(node_type* left, node_type* right) {
    left->merge(right, mutable_allocator());
    if (right->leaf()) {
        if (rightmost_ == right)
            rightmost_ = left;
        delete_leaf_node(right);
    } else {
        delete_internal_node(right);
    }
}

template<typename P>
bool btree<P>::try_merge_or_rebalance(iterator* iter) {
    node_type* parent = iter->node->parent();
    if (iter->node->position() > 0) {
        // Try merging with our left sibling.
        // ----------------------------------
        node_type* left = parent->child(iter->node->position() - 1);
        assert(left->max_count() == kNodeValues);
        if ((1 + left->count() + iter->node->count()) <= kNodeValues) {
            iter->position += 1 + left->count();
            merge_nodes(left, iter->node);
            iter->node = left;
            return true;
        }
    }
    if (iter->node->position() < parent->count()) {
        // Try merging with our right sibling.
        // -----------------------------------
        node_type* right = parent->child(iter->node->position() + 1);
        assert(right->max_count() == kNodeValues);
        if ((1 + iter->node->count() + right->count()) <= kNodeValues) {
            merge_nodes(iter->node, right);
            return true;
        }
        // Try rebalancing with our right sibling. We don't perform rebalancing if
        // we deleted the first element from iter->node and the node is not
        // empty. This is a small optimization for the common pattern of deleting
        // from the front of the tree.
        // -----------------------------------------------------------------------
        if ((right->count() > kMinNodeValues) && ((iter->node->count() == 0) || (iter->position > 0))) {
            int to_move = (right->count() - iter->node->count()) / 2;
            to_move     = (std::min)(to_move, right->count() - 1);
            iter->node->rebalance_right_to_left(to_move, right, mutable_allocator());
            return false;
        }
    }
    if (iter->node->position() > 0) {
        // Try rebalancing with our left sibling. We don't perform rebalancing if
        // we deleted the last element from iter->node and the node is not
        // empty. This is a small optimization for the common pattern of deleting
        // from the back of the tree.
        // ----------------------------------------------------------------------
        node_type* left = parent->child(iter->node->position() - 1);
        if ((left->count() > kMinNodeValues) && ((iter->node->count() == 0) || (iter->position < iter->node->count())))
        {
            int to_move = (left->count() - iter->node->count()) / 2;
            to_move     = (std::min)(to_move, left->count() - 1);
            left->rebalance_left_to_right(to_move, iter->node, mutable_allocator());
            iter->position += to_move;
            return false;
        }
    }
    return false;
}

template<typename P>
void btree<P>::try_shrink() {
    if (root()->count() > 0) {
        return;
    }
    // Deleted the last item on the root node, shrink the height of the tree.
    // ----------------------------------------------------------------------
    if (root()->leaf()) {
        assert(size() == 0);
        delete_leaf_node(root());
        mutable_root() = EmptyNode();
        rightmost_     = EmptyNode();
    } else {
        node_type* child = root()->child(0);
        child->make_root();
        delete_internal_node(root());
        mutable_root() = child;
    }
}

template<typename P>
template<typename IterType>
inline IterType btree<P>::internal_last(IterType iter) {
    assert(iter.node != nullptr);
    while (iter.position == iter.node->count()) {
        iter.position = iter.node->position();
        iter.node     = iter.node->parent();
        if (iter.node->leaf()) {
            iter.node = nullptr;
            break;
        }
    }
    return iter;
}

template<typename P>
template<typename... Args>
inline auto btree<P>::internal_emplace(iterator iter, Args&&... args) -> iterator {
    if (!iter.node->leaf()) {
        // We can't insert on an internal node. Instead, we'll insert after the
        // previous value which is guaranteed to be on a leaf node.
        // --------------------------------------------------------------------
        --iter;
        ++iter.position;
    }
    const int max_count = iter.node->max_count();
    if (iter.node->count() == max_count) {
        // Make room in the leaf for the new item.
        if (max_count < kNodeValues) {
            // Insertion into the root where the root is smaller than the full node
            // size. Simply grow the size of the root node.
            // --------------------------------------------------------------------
            assert(iter.node == root());
            iter.node = new_leaf_root_node((std::min<int>)(kNodeValues, 2 * max_count));
            iter.node->swap(root(), mutable_allocator());
            delete_leaf_node(root());
            mutable_root() = iter.node;
            rightmost_     = iter.node;
        } else {
            rebalance_or_split(&iter);
        }
    }
    iter.node->emplace_value(iter.position, mutable_allocator(), std::forward<Args>(args)...);
    ++size_;
    return iter;
}

template<typename P>
template<typename K>
inline auto btree<P>::internal_locate(const K& key) const -> SearchResult<iterator, is_key_compare_to::value> {
    return internal_locate_impl(key, is_key_compare_to());
}

template<typename P>
template<typename K>
inline auto btree<P>::internal_locate_impl(const K& key, std::false_type /* IsCompareTo */) const
    -> SearchResult<iterator, false> {
    iterator iter(const_cast<node_type*>(root()), 0);
    for (;;) {
        iter.position = iter.node->lower_bound(key, key_comp()).value;
        // NOTE: we don't need to walk all the way down the tree if the keys are
        // equal, but determining equality would require doing an extra comparison
        // on each node on the way down, and we will need to go all the way to the
        // leaf node in the expected case.
        // ----------------------------------------------------------------------
        if (iter.node->leaf()) {
            break;
        }
        iter.node = iter.node->child(iter.position);
    }
    return { iter };
}

template<typename P>
template<typename K>
inline auto btree<P>::internal_locate_impl(const K& key, std::true_type /* IsCompareTo */) const
    -> SearchResult<iterator, true> {
    iterator iter(const_cast<node_type*>(root()), 0);
    for (;;) {
        SearchResult<int, true> res = iter.node->lower_bound(key, key_comp());
        iter.position               = res.value;
        if (res.match == MatchKind::kEq) {
            return { iter, MatchKind::kEq };
        }
        if (iter.node->leaf()) {
            break;
        }
        iter.node = iter.node->child(iter.position);
    }
    return { iter, MatchKind::kNe };
}

template<typename P>
template<typename K>
auto btree<P>::internal_lower_bound(const K& key) const -> iterator {
    iterator iter(const_cast<node_type*>(root()), 0);
    for (;;) {
        iter.position = iter.node->lower_bound(key, key_comp()).value;
        if (iter.node->leaf()) {
            break;
        }
        iter.node = iter.node->child(iter.position);
    }
    return internal_last(iter);
}

template<typename P>
template<typename K>
auto btree<P>::internal_upper_bound(const K& key) const -> iterator {
    iterator iter(const_cast<node_type*>(root()), 0);
    for (;;) {
        iter.position = iter.node->upper_bound(key, key_comp());
        if (iter.node->leaf()) {
            break;
        }
        iter.node = iter.node->child(iter.position);
    }
    return internal_last(iter);
}

template<typename P>
template<typename K>
auto btree<P>::internal_find(const K& key) const -> iterator {
    auto res = internal_locate(key);
    if (res.HasMatch()) {
        if (res.IsEq()) {
            return res.value;
        }
    } else {
        const iterator iter = internal_last(res.value);
        if (iter.node != nullptr && !compare_keys(key, iter.key())) {
            return iter;
        }
    }
    return { nullptr, 0 };
}

template<typename P>
void btree<P>::internal_clear(node_type* node) {
    if (!node->leaf()) {
        for (int i = 0; i <= node->count(); ++i) {
            internal_clear(node->child(i));
        }
        delete_internal_node(node);
    } else {
        delete_leaf_node(node);
    }
}

template<typename P>
typename btree<P>::size_type btree<P>::internal_verify(const node_type* node,
                                                       const key_type*  lo,
                                                       const key_type*  hi) const {
    assert(node->count() > 0);
    assert(node->count() <= node->max_count());
    if (lo) {
        assert(!compare_keys(node->key(0), *lo));
    }
    if (hi) {
        assert(!compare_keys(*hi, node->key(node->count() - 1)));
    }
    for (int i = 1; i < node->count(); ++i) {
        assert(!compare_keys(node->key(i), node->key(i - 1)));
    }
    size_type count = node->count();
    if (!node->leaf()) {
        for (int i = 0; i <= node->count(); ++i) {
            assert(node->child(i) != nullptr);
            assert(node->child(i)->parent() == node);
            assert(node->child(i)->position() == i);
            count += internal_verify(
                node->child(i), (i == 0) ? lo : &node->key(i - 1), (i == node->count()) ? hi : &node->key(i));
        }
    }
    return count;
}

// A common base class for btree_set, btree_map, btree_multiset, and btree_multimap.
// ---------------------------------------------------------------------------------
template<typename Tree>
class btree_container {
    using params_type = typename Tree::params_type;

protected:
    // Alias used for heterogeneous lookup functions.
    // `key_arg<K>` evaluates to `K` when the functors are transparent and to
    // `key_type` otherwise. It permits template argument deduction on `K` for the
    // transparent case.
    // ---------------------------------------------------------------------------
    template<class K>
    using key_arg =
        typename KeyArg<IsTransparent<typename Tree::key_compare>::value>::template type<K, typename Tree::key_type>;

public:
    using key_type               = typename Tree::key_type;
    using value_type             = typename Tree::value_type;
    using size_type              = typename Tree::size_type;
    using difference_type        = typename Tree::difference_type;
    using key_compare            = typename Tree::key_compare;
    using value_compare          = typename Tree::value_compare;
    using allocator_type         = typename Tree::allocator_type;
    using reference              = typename Tree::reference;
    using const_reference        = typename Tree::const_reference;
    using pointer                = typename Tree::pointer;
    using const_pointer          = typename Tree::const_pointer;
    using iterator               = typename Tree::iterator;
    using const_iterator         = typename Tree::const_iterator;
    using reverse_iterator       = typename Tree::reverse_iterator;
    using const_reverse_iterator = typename Tree::const_reverse_iterator;
    using node_type              = typename Tree::node_handle_type;

    // Constructors/assignments.
    btree_container()
        : tree_(key_compare(), allocator_type()) {}
    explicit btree_container(const key_compare& comp, const allocator_type& alloc = allocator_type())
        : tree_(comp, alloc) {}
    btree_container(const btree_container& x)                                                         = default;
    btree_container(btree_container&& x) noexcept                                                     = default;
    btree_container& operator=(const btree_container& x)                                              = default;
    btree_container& operator=(btree_container&& x) noexcept(std::is_nothrow_move_assignable_v<Tree>) = default;

    // Iterator routines.
    iterator               begin() { return tree_.begin(); }
    const_iterator         begin() const { return tree_.begin(); }
    const_iterator         cbegin() const { return tree_.begin(); }
    iterator               end() { return tree_.end(); }
    const_iterator         end() const { return tree_.end(); }
    const_iterator         cend() const { return tree_.end(); }
    reverse_iterator       rbegin() { return tree_.rbegin(); }
    const_reverse_iterator rbegin() const { return tree_.rbegin(); }
    const_reverse_iterator crbegin() const { return tree_.rbegin(); }
    reverse_iterator       rend() { return tree_.rend(); }
    const_reverse_iterator rend() const { return tree_.rend(); }
    const_reverse_iterator crend() const { return tree_.rend(); }

    // Lookup routines.
    // ----------------
    template<typename K = key_type>
    size_type count(const key_arg<K>& key) const {
        auto equal_range = this->equal_range(key);
        return std::distance(equal_range.first, equal_range.second);
    }
    template<typename K = key_type>
    iterator find(const key_arg<K>& key) {
        return tree_.find(key);
    }
    template<typename K = key_type>
    const_iterator find(const key_arg<K>& key) const {
        return tree_.find(key);
    }

    template<typename K = key_type>
    bool contains(const key_arg<K>& key) const {
        return find(key) != end();
    }

    template<typename K = key_type>
    iterator lower_bound(const key_arg<K>& key) {
        return tree_.lower_bound(key);
    }

    template<typename K = key_type>
    const_iterator lower_bound(const key_arg<K>& key) const {
        return tree_.lower_bound(key);
    }

    template<typename K = key_type>
    iterator upper_bound(const key_arg<K>& key) {
        return tree_.upper_bound(key);
    }

    template<typename K = key_type>
    const_iterator upper_bound(const key_arg<K>& key) const {
        return tree_.upper_bound(key);
    }

    template<typename K = key_type>
    std::pair<iterator, iterator> equal_range(const key_arg<K>& key) {
        return tree_.equal_range(key);
    }

    template<typename K = key_type>
    std::pair<const_iterator, const_iterator> equal_range(const key_arg<K>& key) const {
        return tree_.equal_range(key);
    }

    iterator erase(const_iterator iter) { return tree_.erase(iterator(iter)); }
    iterator erase(iterator iter) { return tree_.erase(iter); }
    iterator erase(const_iterator first, const_iterator last) {
        return tree_.erase(iterator(first), iterator(last)).second;
    }

    template<typename K = key_type>
    size_type erase(const key_arg<K>& key) {
        auto equal_range = this->equal_range(key);
        return tree_.erase_range(equal_range.first, equal_range.second).first;
    }
    node_type extract(iterator position) {
        // Use Move instead of Transfer, because the rebalancing code expects to
        // have a valid object to scribble metadata bits on top of.
        // ---------------------------------------------------------------------
        auto node = CommonAccess::Move<node_type>(get_allocator(), position.slot());
        erase(position);
        return node;
    }

    node_type extract(const_iterator position) { return extract(iterator(position)); }

public:
    void clear() { tree_.clear(); }
    void swap(btree_container& x) { tree_.swap(x.tree_); }
    void verify() const { tree_.verify(); }

    size_type size() const { return tree_.size(); }
    size_type max_size() const { return tree_.max_size(); }
    bool      empty() const { return tree_.empty(); }

    friend bool operator==(const btree_container& x, const btree_container& y) {
        return x.size() == y.size() && std::equal(x.begin(), x.end(), y.begin());
    }

    friend bool operator!=(const btree_container& x, const btree_container& y) { return !(x == y); }

    friend bool operator<(const btree_container& x, const btree_container& y) {
        return std::lexicographical_compare(x.begin(), x.end(), y.begin(), y.end());
    }

    friend bool operator>(const btree_container& x, const btree_container& y) { return y < x; }

    friend bool operator<=(const btree_container& x, const btree_container& y) { return !(y < x); }

    friend bool operator>=(const btree_container& x, const btree_container& y) { return !(x < y); }

    // The allocator used by the btree.
    allocator_type get_allocator() const { return tree_.get_allocator(); }

    // The key comparator used by the btree.
    key_compare   key_comp() const { return tree_.key_comp(); }
    value_compare value_comp() const { return tree_.value_comp(); }

    // Support absl::Hash.
    template<typename State>
    friend State AbslHashValue(State h, const btree_container& b) {
        for (const auto& v : b) {
            h = State::combine(std::move(h), v);
        }
        return State::combine(std::move(h), b.size());
    }

protected:
    Tree tree_;
};

// A common base class for btree_set and btree_map.
// ------------------------------------------------
template<typename Tree>
class btree_set_container : public btree_container<Tree> {
    using super_type        = btree_container<Tree>;
    using params_type       = typename Tree::params_type;
    using init_type         = typename params_type::init_type;
    using is_key_compare_to = typename params_type::is_key_compare_to;
    friend class BtreeNodePeer;

protected:
    template<class K>
    using key_arg = typename super_type::template key_arg<K>;

public:
    using key_type           = typename Tree::key_type;
    using value_type         = typename Tree::value_type;
    using size_type          = typename Tree::size_type;
    using key_compare        = typename Tree::key_compare;
    using allocator_type     = typename Tree::allocator_type;
    using iterator           = typename Tree::iterator;
    using const_iterator     = typename Tree::const_iterator;
    using node_type          = typename super_type::node_type;
    using insert_return_type = InsertReturnType<iterator, node_type>;
    using super_type::super_type;
    btree_set_container() {}

    template<class InputIterator>
    btree_set_container(InputIterator         b,
                        InputIterator         e,
                        const key_compare&    comp  = key_compare(),
                        const allocator_type& alloc = allocator_type())
        : super_type(comp, alloc) {
        insert(b, e);
    }

    btree_set_container(std::initializer_list<init_type> init,
                        const key_compare&               comp  = key_compare(),
                        const allocator_type&            alloc = allocator_type())
        : btree_set_container(init.begin(), init.end(), comp, alloc) {}

    btree_set_container(std::initializer_list<init_type> init, const allocator_type& alloc)
        : btree_set_container(init.begin(), init.end(), alloc) {}

    // Lookup routines.
    // ----------------
    template<typename K = key_type>
    size_type count(const key_arg<K>& key) const {
        return this->tree_.count_unique(key);
    }

    // Insertion routines.
    // -------------------
    std::pair<iterator, bool> insert(const value_type& x) { return this->tree_.insert_unique(params_type::key(x), x); }
    std::pair<iterator, bool> insert(value_type&& x) {
        return this->tree_.insert_unique(params_type::key(x), std::move(x));
    }
    template<typename... Args>
    std::pair<iterator, bool> emplace(Args&&... args) {
        init_type v(std::forward<Args>(args)...);
        return this->tree_.insert_unique(params_type::key(v), std::move(v));
    }
    iterator insert(const_iterator hint, const value_type& x) {
        return this->tree_.insert_hint_unique(iterator(hint), params_type::key(x), x).first;
    }
    iterator insert(const_iterator hint, value_type&& x) {
        return this->tree_.insert_hint_unique(iterator(hint), params_type::key(x), std::move(x)).first;
    }

    template<typename... Args>
    iterator emplace_hint(const_iterator hint, Args&&... args) {
        init_type v(std::forward<Args>(args)...);
        return this->tree_.insert_hint_unique(iterator(hint), params_type::key(v), std::move(v)).first;
    }

    template<typename InputIterator>
    void insert(InputIterator b, InputIterator e) {
        this->tree_.insert_iterator_unique(b, e);
    }

    void insert(std::initializer_list<init_type> init) { this->tree_.insert_iterator_unique(init.begin(), init.end()); }

    insert_return_type insert(node_type&& node) {
        if (!node)
            return { this->end(), false, node_type() };
        std::pair<iterator, bool> res =
            this->tree_.insert_unique(params_type::key(CommonAccess::GetSlot(node)), CommonAccess::GetSlot(node));
        if (res.second) {
            CommonAccess::Destroy(&node);
            return { res.first, true, node_type() };
        } else {
            return { res.first, false, std::move(node) };
        }
    }

    iterator insert(const_iterator hint, node_type&& node) {
        if (!node)
            return this->end();
        std::pair<iterator, bool> res = this->tree_.insert_hint_unique(
            iterator(hint), params_type::key(CommonAccess::GetSlot(node)), CommonAccess::GetSlot(node));
        if (res.second)
            CommonAccess::Destroy(&node);
        return res.first;
    }

    template<typename K = key_type>
    size_type erase(const key_arg<K>& key) {
        return this->tree_.erase_unique(key);
    }
    using super_type::erase;

    template<typename K = key_type>
    node_type extract(const key_arg<K>& key) {
        auto it = this->find(key);
        return it == this->end() ? node_type() : extract(it);
    }

    using super_type::extract;

    // Merge routines.
    // Moves elements from `src` into `this`. If the element already exists in
    // `this`, it is left unmodified in `src`.
    // -----------------------------------------------------------------------
    template<typename T,
             typename std::enable_if_t<std::conjunction_v<std::is_same<value_type, typename T::value_type>,
                                                          std::is_same<allocator_type, typename T::allocator_type>,
                                                          std::is_same<typename params_type::is_map_container,
                                                                       typename T::params_type::is_map_container>>,
                                       int> = 0>
    void merge(btree_container<T>& src) { // NOLINT
        for (auto src_it = src.begin(); src_it != src.end();) {
            if (insert(std::move(*src_it)).second) {
                src_it = src.erase(src_it);
            } else {
                ++src_it;
            }
        }
    }

    template<typename T,
             typename std::enable_if_t<std::conjunction_v<std::is_same<value_type, typename T::value_type>,
                                                          std::is_same<allocator_type, typename T::allocator_type>,
                                                          std::is_same<typename params_type::is_map_container,
                                                                       typename T::params_type::is_map_container>>,
                                       int> = 0>
    void merge(btree_container<T>&& src) {
        merge(src);
    }
};

// Base class for btree_map.
// -------------------------
template<typename Tree>
class btree_map_container : public btree_set_container<Tree> {
    using super_type  = btree_set_container<Tree>;
    using params_type = typename Tree::params_type;

protected:
    template<class K>
    using key_arg = typename super_type::template key_arg<K>;

public:
    using key_type       = typename Tree::key_type;
    using mapped_type    = typename params_type::mapped_type;
    using value_type     = typename Tree::value_type;
    using key_compare    = typename Tree::key_compare;
    using allocator_type = typename Tree::allocator_type;
    using iterator       = typename Tree::iterator;
    using const_iterator = typename Tree::const_iterator;

    // Inherit constructors.
    // ---------------------
    using super_type::super_type;
    btree_map_container() {}

    // Insertion routines.
    // -------------------
    template<typename... Args>
    std::pair<iterator, bool> try_emplace(const key_type& k, Args&&... args) {
        return this->tree_.insert_unique(
            k, std::piecewise_construct, std::forward_as_tuple(k), std::forward_as_tuple(std::forward<Args>(args)...));
    }
    template<typename... Args>
    std::pair<iterator, bool> try_emplace(key_type&& k, Args&&... args) {
        // Note: `key_ref` exists to avoid a ClangTidy warning about moving from `k`
        // and then using `k` unsequenced. This is safe because the move is into a
        // forwarding reference and insert_unique guarantees that `key` is never
        // referenced after consuming `args`.
        // ------------------------------------------------------------------------
        const key_type& key_ref = k;
        return this->tree_.insert_unique(key_ref,
                                         std::piecewise_construct,
                                         std::forward_as_tuple(std::move(k)),
                                         std::forward_as_tuple(std::forward<Args>(args)...));
    }
    template<typename... Args>
    iterator try_emplace(const_iterator hint, const key_type& k, Args&&... args) {
        return this->tree_
            .insert_hint_unique(iterator(hint),
                                k,
                                std::piecewise_construct,
                                std::forward_as_tuple(k),
                                std::forward_as_tuple(std::forward<Args>(args)...))
            .first;
    }
    template<typename... Args>
    iterator try_emplace(const_iterator hint, key_type&& k, Args&&... args) {
        // Note: `key_ref` exists to avoid a ClangTidy warning about moving from `k`
        // and then using `k` unsequenced. This is safe because the move is into a
        // forwarding reference and insert_hint_unique guarantees that `key` is
        // never referenced after consuming `args`.
        // -------------------------------------------------------------------------
        const key_type& key_ref = k;
        return this->tree_
            .insert_hint_unique(iterator(hint),
                                key_ref,
                                std::piecewise_construct,
                                std::forward_as_tuple(std::move(k)),
                                std::forward_as_tuple(std::forward<Args>(args)...))
            .first;
    }
    mapped_type& operator[](const key_type& k) { return try_emplace(k).first->second; }
    mapped_type& operator[](key_type&& k) { return try_emplace(std::move(k)).first->second; }

    template<typename K = key_type>
    mapped_type& at(const key_arg<K>& key) {
        auto it = this->find(key);
        if (it == this->end())
            ThrowStdOutOfRange("gtl::btree_map::at");
        return it->second;
    }
    template<typename K = key_type>
    const mapped_type& at(const key_arg<K>& key) const {
        auto it = this->find(key);
        if (it == this->end())
            ThrowStdOutOfRange("gtl::btree_map::at");
        return it->second;
    }
};

// A common base class for btree_multiset and btree_multimap.
// ----------------------------------------------------------
template<typename Tree>
class btree_multiset_container : public btree_container<Tree> {
    using super_type        = btree_container<Tree>;
    using params_type       = typename Tree::params_type;
    using init_type         = typename params_type::init_type;
    using is_key_compare_to = typename params_type::is_key_compare_to;

    template<class K>
    using key_arg = typename super_type::template key_arg<K>;

public:
    using key_type       = typename Tree::key_type;
    using value_type     = typename Tree::value_type;
    using size_type      = typename Tree::size_type;
    using key_compare    = typename Tree::key_compare;
    using allocator_type = typename Tree::allocator_type;
    using iterator       = typename Tree::iterator;
    using const_iterator = typename Tree::const_iterator;
    using node_type      = typename super_type::node_type;

    // Inherit constructors.
    // ---------------------
    using super_type::super_type;
    btree_multiset_container() {}

    // Range constructor.
    // ------------------
    template<class InputIterator>
    btree_multiset_container(InputIterator         b,
                             InputIterator         e,
                             const key_compare&    comp  = key_compare(),
                             const allocator_type& alloc = allocator_type())
        : super_type(comp, alloc) {
        insert(b, e);
    }

    // Initializer list constructor.
    // -----------------------------
    btree_multiset_container(std::initializer_list<init_type> init,
                             const key_compare&               comp  = key_compare(),
                             const allocator_type&            alloc = allocator_type())
        : btree_multiset_container(init.begin(), init.end(), comp, alloc) {}

    // Lookup routines.
    // ----------------
    template<typename K = key_type>
    size_type count(const key_arg<K>& key) const {
        return this->tree_.count_multi(key);
    }

    // Insertion routines.
    // -------------------
    iterator insert(const value_type& x) { return this->tree_.insert_multi(x); }
    iterator insert(value_type&& x) { return this->tree_.insert_multi(std::move(x)); }
    iterator insert(const_iterator hint, const value_type& x) {
        return this->tree_.insert_hint_multi(iterator(hint), x);
    }
    iterator insert(const_iterator hint, value_type&& x) {
        return this->tree_.insert_hint_multi(iterator(hint), std::move(x));
    }
    template<typename InputIterator>
    void insert(InputIterator b, InputIterator e) {
        this->tree_.insert_iterator_multi(b, e);
    }
    void insert(std::initializer_list<init_type> init) { this->tree_.insert_iterator_multi(init.begin(), init.end()); }
    template<typename... Args>
    iterator emplace(Args&&... args) {
        return this->tree_.insert_multi(init_type(std::forward<Args>(args)...));
    }
    template<typename... Args>
    iterator emplace_hint(const_iterator hint, Args&&... args) {
        return this->tree_.insert_hint_multi(iterator(hint), init_type(std::forward<Args>(args)...));
    }
    iterator insert(node_type&& node) {
        if (!node)
            return this->end();
        iterator res =
            this->tree_.insert_multi(params_type::key(CommonAccess::GetSlot(node)), CommonAccess::GetSlot(node));
        CommonAccess::Destroy(&node);
        return res;
    }
    iterator insert(const_iterator hint, node_type&& node) {
        if (!node)
            return this->end();
        iterator res =
            this->tree_.insert_hint_multi(iterator(hint), std::move(params_type::element(CommonAccess::GetSlot(node))));
        CommonAccess::Destroy(&node);
        return res;
    }

    // Deletion routines.
    // ------------------
    template<typename K = key_type>
    size_type erase(const key_arg<K>& key) {
        return this->tree_.erase_multi(key);
    }
    using super_type::erase;

    // Node extraction routines.
    template<typename K = key_type>
    node_type extract(const key_arg<K>& key) {
        auto it = this->find(key);
        return it == this->end() ? node_type() : extract(it);
    }
    using super_type::extract;

    // Merge routines.
    // Moves all elements from `src` into `this`.
    // ------------------------------------------
    template<typename T,
             typename std::enable_if_t<std::conjunction_v<std::is_same<value_type, typename T::value_type>,
                                                          std::is_same<allocator_type, typename T::allocator_type>,
                                                          std::is_same<typename params_type::is_map_container,
                                                                       typename T::params_type::is_map_container>>,
                                       int> = 0>
    void merge(btree_container<T>& src) { // NOLINT
        insert(std::make_move_iterator(src.begin()), std::make_move_iterator(src.end()));
        src.clear();
    }

    template<typename T,
             typename std::enable_if_t<std::conjunction_v<std::is_same<value_type, typename T::value_type>,
                                                          std::is_same<allocator_type, typename T::allocator_type>,
                                                          std::is_same<typename params_type::is_map_container,
                                                                       typename T::params_type::is_map_container>>,
                                       int> = 0>
    void merge(btree_container<T>&& src) {
        merge(src);
    }
};

// A base class for btree_multimap.
// --------------------------------
template<typename Tree>
class btree_multimap_container : public btree_multiset_container<Tree> {
    using super_type  = btree_multiset_container<Tree>;
    using params_type = typename Tree::params_type;

public:
    using mapped_type = typename params_type::mapped_type;

    // Inherit constructors.
    using super_type::super_type;
    btree_multimap_container() {}
};

} // namespace priv

// ----------------------------------------------------------------------
//  btree_set - default values in phmap_fwd_decl.hpp
// ----------------------------------------------------------------------
template<typename Key, typename Compare, typename Alloc>
class btree_set
    : public priv::btree_set_container<
          priv::btree<priv::set_params<Key, Compare, Alloc, /*TargetNodeSize=*/256, /*Multi=*/false>>> {
    using Base = typename btree_set::btree_set_container;

public:
    btree_set() {}
    using Base::Base;
    using Base::begin;
    using Base::cbegin;
    using Base::cend;
    using Base::clear;
    using Base::contains;
    using Base::count;
    using Base::emplace;
    using Base::emplace_hint;
    using Base::empty;
    using Base::end;
    using Base::equal_range;
    using Base::erase;
    using Base::extract;
    using Base::find;
    using Base::get_allocator;
    using Base::insert;
    using Base::key_comp;
    using Base::lower_bound;
    using Base::max_size;
    using Base::merge;
    using Base::size;
    using Base::swap;
    using Base::upper_bound;
    using Base::value_comp;
};

// Swaps the contents of two `gtl::btree_set` containers.
// -------------------------------------------------------
template<typename K, typename C, typename A>
void swap(btree_set<K, C, A>& x, btree_set<K, C, A>& y) {
    return x.swap(y);
}

// Erases all elements that satisfy the predicate pred from the container.
// ----------------------------------------------------------------------
template<typename K, typename C, typename A, typename Pred>
void erase_if(btree_set<K, C, A>& set, Pred pred) {
    for (auto it = set.begin(); it != set.end();) {
        if (pred(*it)) {
            it = set.erase(it);
        } else {
            ++it;
        }
    }
}

// ----------------------------------------------------------------------
//  btree_multiset - default values in phmap_fwd_decl.hpp
// ----------------------------------------------------------------------
template<typename Key, typename Compare, typename Alloc>
class btree_multiset
    : public priv::btree_multiset_container<
          priv::btree<priv::set_params<Key, Compare, Alloc, /*TargetNodeSize=*/256, /*Multi=*/true>>> {
    using Base = typename btree_multiset::btree_multiset_container;

public:
    btree_multiset() {}
    using Base::Base;
    using Base::begin;
    using Base::cbegin;
    using Base::cend;
    using Base::clear;
    using Base::contains;
    using Base::count;
    using Base::emplace;
    using Base::emplace_hint;
    using Base::empty;
    using Base::end;
    using Base::equal_range;
    using Base::erase;
    using Base::extract;
    using Base::find;
    using Base::get_allocator;
    using Base::insert;
    using Base::key_comp;
    using Base::lower_bound;
    using Base::max_size;
    using Base::merge;
    using Base::size;
    using Base::swap;
    using Base::upper_bound;
    using Base::value_comp;
};

// Swaps the contents of two `gtl::btree_multiset` containers.
// ------------------------------------------------------------
template<typename K, typename C, typename A>
void swap(btree_multiset<K, C, A>& x, btree_multiset<K, C, A>& y) {
    return x.swap(y);
}

// Erases all elements that satisfy the predicate pred from the container.
// ----------------------------------------------------------------------
template<typename K, typename C, typename A, typename Pred>
void erase_if(btree_multiset<K, C, A>& set, Pred pred) {
    for (auto it = set.begin(); it != set.end();) {
        if (pred(*it)) {
            it = set.erase(it);
        } else {
            ++it;
        }
    }
}

// ----------------------------------------------------------------------
//  btree_map - default values in phmap_fwd_decl.hpp
// ----------------------------------------------------------------------
template<typename Key, typename Value, typename Compare, typename Alloc>
class btree_map
    : public priv::btree_map_container<
          priv::btree<priv::map_params<Key, Value, Compare, Alloc, /*TargetNodeSize=*/256, /*Multi=*/false>>> {
    using Base = typename btree_map::btree_map_container;

public:
    btree_map() {}
    using Base::at;
    using Base::Base;
    using Base::begin;
    using Base::cbegin;
    using Base::cend;
    using Base::clear;
    using Base::contains;
    using Base::count;
    using Base::emplace;
    using Base::emplace_hint;
    using Base::empty;
    using Base::end;
    using Base::equal_range;
    using Base::erase;
    using Base::extract;
    using Base::find;
    using Base::insert;
    using Base::lower_bound;
    using Base::max_size;
    using Base::merge;
    using Base::size;
    using Base::swap;
    using Base::try_emplace;
    using Base::upper_bound;
    using Base::operator[];
    using Base::get_allocator;
    using Base::key_comp;
    using Base::value_comp;
};

// Swaps the contents of two `gtl::btree_map` containers.
// -------------------------------------------------------
template<typename K, typename V, typename C, typename A>
void swap(btree_map<K, V, C, A>& x, btree_map<K, V, C, A>& y) {
    return x.swap(y);
}

// ----------------------------------------------------------------------
template<typename K, typename V, typename C, typename A, typename Pred>
void erase_if(btree_map<K, V, C, A>& map, Pred pred) {
    for (auto it = map.begin(); it != map.end();) {
        if (pred(*it)) {
            it = map.erase(it);
        } else {
            ++it;
        }
    }
}

// ----------------------------------------------------------------------
//  btree_multimap - default values in phmap_fwd_decl.hpp
// ----------------------------------------------------------------------
template<typename Key, typename Value, typename Compare, typename Alloc>
class btree_multimap
    : public priv::btree_multimap_container<
          priv::btree<priv::map_params<Key, Value, Compare, Alloc, /*TargetNodeSize=*/256, /*Multi=*/true>>> {
    using Base = typename btree_multimap::btree_multimap_container;

public:
    btree_multimap() {}
    using Base::Base;
    using Base::begin;
    using Base::cbegin;
    using Base::cend;
    using Base::clear;
    using Base::contains;
    using Base::count;
    using Base::emplace;
    using Base::emplace_hint;
    using Base::empty;
    using Base::end;
    using Base::equal_range;
    using Base::erase;
    using Base::extract;
    using Base::find;
    using Base::get_allocator;
    using Base::insert;
    using Base::key_comp;
    using Base::lower_bound;
    using Base::max_size;
    using Base::merge;
    using Base::size;
    using Base::swap;
    using Base::upper_bound;
    using Base::value_comp;
};

// Swaps the contents of two `gtl::btree_multimap` containers.
// ------------------------------------------------------------
template<typename K, typename V, typename C, typename A>
void swap(btree_multimap<K, V, C, A>& x, btree_multimap<K, V, C, A>& y) {
    return x.swap(y);
}

// Erases all elements that satisfy the predicate pred from the container.
// ----------------------------------------------------------------------
template<typename K, typename V, typename C, typename A, typename Pred>
void erase_if(btree_multimap<K, V, C, A>& map, Pred pred) {
    for (auto it = map.begin(); it != map.end();) {
        if (pred(*it)) {
            it = map.erase(it);
        } else {
            ++it;
        }
    }
}

} // namespace btree

#ifdef _MSC_VER
    #pragma warning(pop)
#endif

#endif // gtl_btree_container_hpp_
